(CNN) -- U.S. Secretary of State Hillary Clinton warned Iran on Sunday to not view the withdrawal of U.S. combat troops from Iraq as an opportunity to try to build its influence in the country.
"No one, most particularly Iran, should miscalculate about our continuing commitment to and with the Iraqis going forward," she told CNN's "State of the Union" when asked whether Iran's relationship with Iraq is a concern.
In an interview last week with CNN's Fareed Zakaria, Iranian President Mahmoud Ahmadinejad said his country will not increase its involvement with Iraq because of the U.S. withdrawal. "I don't think there is going to be any change," Ahmadinejad said.
Zakaria mentioned U.S. President Barack Obama's recent announcement that virtually all U.S. troops will be out of Iraq by the end of the year. He also asked Ahmadinejad whether Iran will increase its efforts to train the Iraqi army or provide greater support with training.
"I think this is going to be a very good idea and it should have been done sooner, maybe seven or eight years ago. And they could avoid killing so many Iraqis people or Americans as well. I think they should have done it much earlier," Ahmadinejad said. "But the people and Iraqi government did not accept the increased presence of the Americans. The Iraqi government is independent and sovereign. They should decide how to provide training for their military personal. Now, we should wait for the decision of the Iraqi government."
Clinton, speaking to CNN from Uzbekistan, emphasized that the United States will continue a training mission in Iraq, as it has with some other countries. "What we will not have are combat troops and bases," she said. The United States will also have "a very robust diplomatic presence," as envisioned in agreements dating back to the previous administration of President George W. Bush, she said.
"Iran would be badly miscalculating if they did not look at the entire region and all of our presence in many countries in the region, both in bases, in training with NATO allies like Turkey. So I'm used to the president of Iran saying all kinds of things, but I think it's important to set the record straight."
Sen. John McCain of Arizona, the ranking Republican on the Senate Armed Services Committee, assailed the U.S. withdrawal.
"I think it's a serious mistake. And there was never really serious negotiations between the administration and the Iraqis," he said on ABC's "This Week." "They could have clearly made an arrangement for U.S. troops."
Speaking from Jordan, McCain complained that the withdrawal plan "is viewed in the region as a victory for the Iranians. And I don't think there's any doubt there is." He added, "I'm very, very concerned about increased Iranian influence in Iraq."
"I think the fact that we have other bases in the region would have very little impact on Iraq itself," McCain said.
He cited Muqtada al-Sadr, the influential Iraqi Shiite cleric, as a potential conduit for Iranian influence, and said he believes Iraqi Prime Minister Nuri al-Maliki is "leaning more and more toward alliances" with Iran.
Sen. Lindsey Graham, R- South Carolina, who also serves on the Armed Services Committee, told "Fox News Sunday" that he believes Obama has "made poor, dangerous policy questions at the strategic level when it comes to Iraq."
Rejecting Clinton's remark on the same program that Obama has exhibited "smart leadership in a complex world," Graham said he believes that "Iraq and Afghanistan are being run out of Chicago, not Washington, in terms of decisions," an apparent reference to Obama's re-election campaign, which is being run out of Chicago.
Graham added, "not able to close the deal in Iraq is a serious mistake. Celebrating leaving with no troops behind is a serious mistake."
CNN's Mitra Mobasherat contributed to this report.