DETROIT (Reuters) - Republican presidential candidate John McCain commented on Friday on the unannounced timing of a high-security trip by Barack Obama to Iraq, saying he believed his Democratic rival was going this weekend.

But McCain’s spokesman said the Arizona senator knew nothing about Obama’s schedule. Obama said last month he would go to both Iraq and Afghanistan soon. But his campaign has given no dates, seeking to cloak the trip in a measure of secrecy for security reasons.

“I believe that either today or tomorrow -- and I’m not privy to his schedule -- Sen. Obama will be landing in Iraq with some other senators” who make up a congressional delegation, McCain said at a Republican fund-raiser.

McCain’s campaign spokeswoman Brooke Buchanan insisted to reporters later: “He doesn’t know when he’s going. He’s not privy to that information. He was speaking in broader terms, about when Obama does land in Iraq.”

McCain has been sharply critical of Obama, particularly for announcing his support for withdrawing U.S. troops from Iraq in a 16-month timetable, before actually having visited the country or meeting with commanders on the ground.

“Sen. Obama is going to arrive in Baghdad in a much, much safer and secure environment than the one that he would’ve encountered before we started the surge,” McCain said, referring to a boost in U.S. troop numbers in Iraq that began last year.

McCain, who has made national security and foreign policy the centerpiece of his campaign for the November 4 election, has pressed Obama to visit Iraq.

Robert Gibbs, a top aide to Obama, had no comment on McCain’s remark.

The Obama campaign has announced he would soon visit Jordan, Israel, London, Paris and Berlin but has made public only the barest of details.

McCain, a strong backer of the U.S. troop build-up that President George W. Bush launched in early 2007, said that while in Iraq Obama should thank the top U.S. military officer, Gen. David Petraeus, for the current strategy and “thank him for his leadership.”

He said Obama should express his regrets to Petraeus for failing to support a non-binding Senate resolution last year condemning an advertisement in The New York Times by a liberal group that mocked Petraeus as “Gen. Betray-us.”

“So he’ll land in a very different Baghdad. And we have succeeded in Iraq, and we will win if we continue with this strategy that we are pursuing,” McCain said.

Republican Sen. Chuck Hagel of Nebraska and Democratic Sen. Jack Reed of Rhode Island were to be part of the congressional delegation with Obama.

(Reporting by Steve Holland, editing by Alan Elsner and Frances Kerry)