Sen. Ted Cruz (R-Tex.) pauses during his speech at an election-night watch party Tuesday in Houston. (David J. Phillip/AP)

This post has been updated

HOUSTON — Sen. Ted Cruz is facing criticism for appointing Frank Gaffney, who is known for holding extreme anti-Muslim views, to his foreign policy team.

Gaffney is part of a 23-member foreign policy team Cruz rolled out Thursday. It is a disparate group of advisers who will help the presidential candidate formulate his stance on global issues.

The group includes former members of the Ronald Reagan and George W. Bush administrations, as well as Gaffney and two others who work  at his think tank, the Center for Security Policy, which has been designated a hate group by the Southern Poverty Law Center. Gaffney said President Obama could be "considered America's first Muslim president."

The Southern Poverty Law Center accuses Gaffney of being "one of America’s most notorious Islamophobes." Donald Trump cited a study commissioned by Gaffney's think tank to back up his proposal to bar Muslims from entering the United States.

"Frank Gaffney has no business advising on matters of foreign policy," said Richard Cohen, president of the Southern Poverty Law Center.

"Gaffney and his Center for Security Policy have long equated Islam with terrorism. Their sole mission is to stoke fear about American Muslims and Muslims around the world. Providing him with a national platform is wildly inappropriate."

The Council on American Islamic Relations, known as CAIR, is calling on Cruz to drop Gaffney and Retired Lt. Gen. William "Jerry" Boykin, who has said there should be no mosques allowed in America.

“Who a candidate picks for his or her advisers says volumes about that candidate’s worldview. By choosing infamous Islamophobes as foreign policy advisers, Senator Cruz indicates that he subscribes to their conspiratorial worldview and to the anti-Muslim bigotry that would inevitably shape their policy recommendations," said CAIR national Executive Director Nihad Awad. "We ask Senator Cruz to drop any adviser who has a past history of promoting conspiracy theories or religious bigotry.”

Cruz's campaign did not immediately respond to a request for comment.

Cruz's team also includes Elliott Abrams, who served as an assistant secretary of state in the Reagan administration and as deputy national security adviser under President George W. Bush. Abrams has said Trump's proposal to bar Muslims is "senseless" and "dangerous."

Cruz is attempting to marry the insurgent and establishment wings of the Republican Party in an effort to thwart Trump.

"I am honored and humbled to have a range of respected voices willing to offer their best advice,” Cruz said in a statement.

Cruz's main foreign policy adviser in the Senate and on the campaign has been Victoria Coates, a former art historian.

On the campaign trail, Cruz often warns of the dangers of the "Obama-Clinton foreign policy," which he says is one of appeasement toward enemies leading to a weakening of the United States.

Cruz has attempted to thread the needle on foreign policy to appeal to both the more hawkish and the libertarian-leaning factions of the GOP. He has said that the United States should "carpet-bomb" the Islamic State but has warned against unnecessary foreign interventions. He has said that strongmen such as Moammar Gaddafi should have been left in power, because toppling them led to a vacuum that the Islamic State was able to exploit. He has also called for the U.S. military to be expanded.

The senator from Texas is staunchly against Obama's Iranian nuclear deal, vowing to undo it if he is elected to the Oval Office.

"Senator Cruz has a perfect record of support for Israel in the Senate, and he has made it clear that he believes a strong Israel is America's key ally and asset in the Middle East," Abrams said in a statement.

The list Cruz announced Thursday also includes Clare Lopez, who works for Gaffney's think tank; Andy McCarthy, who led the prosecution of Omar Abdel Rahman, who helped orchestrate the bombing of the World Trade Center in 1993; Randy Fort, an official in the Reagan administration and both Bush administration; and former senator Jim Talent (R) of Missouri.