Following the deadly Paris attacks, several U.S. governors say they would not allow Syrian refugees to settle in their states. (Reuters)

Governors across the country are scrambling to close off their states to resettled Syrian refugees in the wake of the deadly terror attacks in Paris that are linked to Islamic State extremists.

The list of states climbed quickly to 23 by Monday evening, after President Obama said that the U.S. would continue to accept refugees and denounced efforts to stop those fleeing violence from coming to the United States as "shameful."

Governors of Illinois, Ohio, Florida, North Carolina, South Carolina, Maine, Iowa, Oklahoma, Wisconsin, New Jersey, New Hampshire, Arizona, Indiana, Massachusetts, Idaho, Louisiana, Michigan, Alabama, Texas, Kansas, Georgia, Mississippi, and Arkansas — a majority of them Republican — have said that they are seeking to stop the relocation of new Syrian refugees to their states out of fear that violent extremists posing as refugees might gain entry to the country.

New Hampshire Gov. Maggie Hassan, who is also challenging Sen. Kelly Ayotte (R-N.H.) for her Senate seat, is the first Democrat to express support for halting the flow of refugees to the U.S. pending further assurances that the refugee vetting process is adequate.

"The Governor has always made clear that we must ensure robust refugee screening to protect American citizens, and the Governor believes that the federal government should halt acceptance of refugees from Syria until intelligence and defense officials can assure that the process for vetting all refugees, including those from Syria, is as strong as possible to ensure the safety of the American people," William Hinkle, a spokesman for Hassan, said in a statement.

At the same time, several acknowledged that they do not have the ability to stop the federal government from accepting and financing the resettlement of refugees to the United States. They have also sought reassurances that the process used to screen refugees is adequate.

Non-profit agencies who work with the federal government to resettle refugees in the U.S. confirmed that while the cooperation of states and localities helps in the process, no governor can impede the movement of refugees in the U.S. once they have legal status.

“Governors and state officials do not have the capability to prevent a refugee who is here and admitted lawfully to the U.S. from residing in their state. It is not something they can do,” said Lucy Carrigan, a spokeswoman for the International Rescue Committee. "There is a close collaboration with governors and mayors and community leaders about the capacity of the area for refugees and where they can go, but once they have legal status, you cannot impede their transit between different states.”

According to the Obama administration, which has stated that it hopes to resettle at least 10,000 Syrian refugees, more than 180 cities and towns have expressed willingness to accept refugees, despite the recent groundswell of opposition from some governors. The U.S. has accepted more than 2,100 refugees from Syria since 2012, most of them in the last year.

[Obama calls idea of screening Syrian refugees based on religion ‘shameful,’ defends White House strategy ]

In Michigan, a state with a large population of Muslims, Gov. Rick Snyder on Sunday noted that the state has a "rich history of immigration" and that extremists "do not reflect the peaceful ways of people of Middle Eastern descent here and around the world."

But, Snyder added, “our first priority is protecting the safety of our residents.”

Michigan will temporarily halt its efforts to accept new refugees until they are able to work with the federal government to review the procedures in place for screening applicants. The move does not single out any specific group of refugees and it would not affect any refugees who are already on their way to the state, a spokesman for Snyder's office said.

"It's not expected to be a prolonged review," Snyder's deputy press secretary Dave Murray said.

The situation has quickly become political, with Republican presidential candidate and Louisiana Gov. Bobby Jindal becoming the first of the governors in the race to block refugees in his own state.

"I just signed an Executive Order instructing state agencies to take all available steps to stop the relocation of Syrian refugees to LA," Jindal tweeted.

Hours after suggesting that she would not stop refugees from entering her state, South Carolina Gov. Nikki Haley changed course. In a letter to Secretary of State John Kerry, Haley wrote that she is requesting that the State Department halt resettlements to South Carolina until she is given assurances that all refugees from Syria have no connections to terrorists.

It is not clear, however, what governors could actually do to stop refugees from resettling in their states. Resettlement applications are handled by the U.S. State Department. The process takes between 18 and 24 months, and applicants are screened by the Department of Homeland Security and interviewed before being approved to relocate to the U.S. And according to human rights activists, they are among the most stringently screened and vetted applicants who enter the country.

In a statement, presidential hopeful and Ohio Gov. John Kasich said that he opposed resettling Syrian refugees in Ohio and has written to Obama asking him to stop sending refugees to his state, suggesting that he does not have the power to unilaterally halt the process himself.

"The governor doesn’t believe the U.S. should accept additional Syrian refugees because security and safety issues cannot be adequately addressed," Kasich spokesman Jim Lynch said. "The governor is writing to the president to ask him to stop, and to ask him to stop resettling them in Ohio."

"We are also looking at what additional steps Ohio can take to stop resettlement of these refugees,” he added.

[Raids spread across France and Belgium amid manhunt for suspects]

Some of the attention has shifted to congressional action that could halt federal funding for refugee resettlement.

In a letter to House Speaker Paul Ryan (R-Wis.) and Senate Majority Leader Mitch McConnell (R-Ky.), Florida Gov. Rick Scott noted that the states would not have the power to halt federal funds from going toward resettling as many as 425 refugees in his state.

"It is our understanding that the state does not have the authority to prevent the federal government from funding the relocation of these Syrian refugees to Florida even without state support," Scott wrote. "Therefore, we are asking the United States Congress to take immediate and aggressive action" to prevent Obama and his administration from funding Syrian refugee relocation to the United States.

Former Arkansas governor Mike Huckabee, another presidential hopeful, said Monday that Ryan should resign if he does not "reject the importation of those fleeing the Middle East."

Congress' hands may also be tied in other ways. Funding for refugee resettlement in 2016 has largely been appropriated, and the money is not divvied up by country of origin.

[How many Syrian and Iraqi refugees were settled in each state since 2012, in 3 maps]

"Our focus  right now is to work with Congress, work with these state and local governments and try to relay their concerns about refugees," said State Department deputy spokesman Mark Toner. "We're aware of these concerns. We're looking at them and we're going to work with local governments to address them.”

Sen. Rand Paul (R-Ky.), another presidential candidate, said he would introduce a bill to stop refugees from countries with jihadist movements from entering the U.S., pending strict background checks.

Another governor in the presidential race, Chris Christie (R-N.J.), told conservative radio host Hugh Hewitt that he would not admit Syrian refugees.

Some presidential candidates, like Sen. Ted Cruz (R-Tex.), have suggested that it is too risky to admit Muslim refugees.

[Rand Paul introduces bill to bar refugees from Syria, subject French citizens to waiting period]

Obama responded at a news conference during the G-20 summit in Turkey that the suggestion was un-American.

"The United States has to step up and do its part," Obama said. "And when I hear folks say that, well, maybe we should just admit the Christians but not the Muslims, when I hear political leaders suggesting that there would be a religious test for which person who's fleeing from a war-torn country is admitted, when some of those folks themselves come from families who benefited from protection when they were fleeing political persecution, that's shameful."

"That's not American, it's not who we are," he added.

President Obama decried the calls from some to stop accepting Syrian refugees after the attacks in Paris, saying it would be "a betrayal of our values." (AP)

At least two Democratic governors have declined to join their Republican counterparts in taking a stance against the refugees.

Pennsylvania Gov. Tom Wolf said his state would not impede migrants from being resettled there, and a spokesman for Virginia Gov. Terry McAuliffe said precautions would be taken to ensure that Virginians are protected.

“With respect to refugees, the governor and his public safety team are in constant communication with federal authorities about all refugee resettlements, including those involving refugees from Syria," said McAuliffe spokesman Brian Coy. "Every refugee who is settled in the U.S. undergoes intensive security screening, and the governor has asked Secretary Moran to ensure that every proper precaution is taken to keep Virginians safe."

Alabama Gov. Robert Bentley noted Sunday that his state had not admitted any refugees, but none would be allowed to settle there in the future.

On Monday, Indiana Gov. Mike Pence ordered state agencies to "suspend the resettlement of additional Syrian refugees" to Indiana "pending assurances from the federal government that proper security measures have been achieved."

"Unless and until the state of Indiana receives assurances that proper security measures are in place, this policy will remain in full force and effect,” Pence added.

[Would Jesus take in Syrian refugees?]

Massachusetts Gov. Charlie Baker echoed the sentiment that his state is seeking additional security assurances from the federal government. “No, I’m not interested in accepting refugees from Syria,” he told reporters. “I would need to know a lot more than I know now before I would agree to do anything.”

In Arkansas, Gov. Asa Hutchinson noted that refugees pose a "risk" to Arkansans, and should be relocated in Europe, Africa or Asia. And in Illinois, Gov. Bruce Rauner said in a statement Monday that the state would temporarily halt the resettlement of refugees after the Paris attacks served as a reminder of "the all-too-real security threats facing America."

Texas Gov. Greg Abbott went further, calling on Obama to halt all plans to accept refugees into the United States entirely.

"Given the tragic attacks in Paris and the threats we have already seen, Texas cannot participate in any program that will result in Syrian refugees — any one of whom could be connected to terrorism — being resettled in Texas," Abbott said in a letter to Obama.

Pam Constable, Carol Morello, and Juliet Eilperin contributed to this report.