Facing criticism that he has not reached out to Republicans negotiating an immigration overhaul, President Obama placed phone calls Tuesday afternoon to three GOP senators involved in an eight-member Senate bipartisan group working on the issue.

FILE - In this March 28, 2012 file photo, Sen. John McCain, R-Ariz. listens during a news conference on Capitol Hill in Washington. McCain said in an interview posted online Friday that "foreign money" was helping fellow Republican Mitt Romney's presidential hopes and singled out one of his ally's most generous supporters. (AP Photo/Jacquelyn Martin, File) Sen. John McCain, R-Ariz. was among the senators called by President Obama. (AP Photo/Jacquelyn Martin, File)

According to White House officials, Obama spoke to Sen. Marco Rubio (R-Fla,), Sen. Lindsey Graham (R-S.C.) and Sen. John McCain (R-Ariz.). Officials said that with each, he discussed "their shared commitment to bipartisan, commonsense immigration reform," and that he commended the senators for "the bipartisan progress that continues to be made by the Gang of Eight on this important issue."

Obama told Republicans that he is supportive of the Senate effort and that he hopes they can bring forward a bill "as soon as possible that reflects shared core principles on reform."

The calls came after Republicans criticized Obama for failing to reach out and after White House staffers tangled with aides to Rubio earlier Tuesday over whether the administration officials have been engaged in the Senate talks. The senators unveiled a bipartisan set of principles to guide reform last month and have said they hope to introduce an immigration bill in March.

After days of slamming the White House over the weekend leak of a draft immigration bill administration officials are preparing in case the Senate process drags, an aide to Rubio said he appreciated receiving Obama's call before the president leaves for Israel late tonight.

"The senator told the president that he feels good about the ongoing negotiations in the Senate, and is hopeful the final product is something that can pass the Senate with strong bipartisan support," Rubio spokesman Alex Conant said.

A spokesman for Graham said the two shared a "short, cordial" conversation. "They discussed the need for immigration reform and why it is important we fix our broken immigration system," spokesman Kevin Bishop said.

White House officials indicated that Obama told the senators that he believes reform should include strengthening border security, as well as creating an earned path to citizenship, holding employers accountable for employing legal workers and streamlining legal immigration.

Obama met with the group's four Democrats -- Sen. Chuck Schumer (D-N.Y.), Sen. Dick Durbin (D-Ill.), Sen. Bob Menendez (D-N.J.) and Sen. Michael Bennet (D-Colo.) -- at the White House last week.

White House officials said Obama did not reach the group's fourth Republican, Sen. Jeff Flake (R-Ariz.), who is traveling, but would speak with him soon.