WASHINGTON — Senator McCain, the Republican from Arizona who will be his party’s candidate for the presidency, is making a visit to Iraq.

Mr. McCain arrived yesterday in Baghdad for meetings with top American and Iraqi officials.

The visit for Mr. McCain carries special significance because his early support for the counteroffensive in late 2006 and early 2007 has emerged as a key selling point for his campaign. The senator was lampooned by many war critics in April when he visited Baghdad and told CNN about the return to normal life there, at a moment when most polls showed Americans believed the war was lost.

News wires are reporting that Mr. McCain will be meeting with the commander of Multi-National Forces in Iraq and the man widely credited with the fall in violence in Baghdad and Anbar, General David Petraeus. Mr. McCain has praised General Petraeus as one of American history’s great generals. But the skilled commander in Baghdad has deliberately stayed neutral on the American political scene. Later this month, General Petraeus and the American ambassador in Iraq, Ryan Crocker, will come to Washington to deliver their latest assessment of the situation in Iraq to Congress.

Democrats have already begun attacking Mr. McCain for traveling with close political allies such as Senator Lindsey Graham, a Republican from South Carolina, and Senator Lieberman, an independent Democrat from Connecticut.

On CNN’s “Late Edition,” Senator Feinstein, a Democrat of California, said, “I think it would have probably been better if he took members who were not so closely identified with his campaign. But this is indicated to be a congressional visit.”

Mr. McCain has said that he is traveling as a member of the Senate Committee on Armed Services, and not as a candidate for the White House.

Coinciding with Mr. McCain’s visit to the Middle East is a trip from Vice President Cheney. His plane left Washington yesterday. Last week, President Bush said he was sending his vice president to follow up on Secretary of State Rice’s trip this month to Israel and its neighbors, to revive the Annapolis peace process. Mr. Cheney is also expected to discuss Iran’s nuclear weapons program. Mr. McCain is expected to stay in Iraq for 24 hours. He said he intended to travel outside of Baghdad. Mr. McCain’s itinerary also includes visits to Israel and Jordan, and then stops in Britain and France.