Barack Obama said Monday he would set a goal of having all U.S. combat brigades out of Iraq by summer 2010 and shift more resources to fighting Al Qaeda in Afghanistan.

In an op-ed in The New York Times, the expected Democratic presidential nominee criticized John McCain and the Bush administration for "refusing to embrace" the idea that Iraqis should take over responsibility for military control of the country and the fight against terrorist and insurgent forces. He also dismissed the troop surge that McCain supported because he said it's been too costly and has not led to Iraqi political reconciliation.

Obama said current U.S. strategy "is not a strategy for success -- it is a strategy for staying that runs contrary to the will of the Iraqi people, the American people and the security interests of the United States. That is why, on my first day in office, I would give the military a new mission: ending this war."

He pointed to Iraqi Prime Minister Nouri Al-Maliki's request for a U.S. timetable for withdrawal as an opportunity to "seize this moment to begin the phased redeployment of combat troops that I have long advocated, and that is needed for long-term success in Iraq and the security interests of the United States."

Sen. Lindsay Graham, R-S.C., speaking on behalf of McCain Monday, took aim at Obama's policies.

"If we had followed his (Obama's) advice, Iraq would have crumbled, Al Qaeda would have won and Iran would gain influence," Graham told reporters on a telephone conference call. It was the second straight day of back-and-forth over Iraq policy between the campaigns.

On July 3, Obama kicked off speculation over where his Iraq policy would go after he said he might "refine" his Iraq policy following an upcoming planned trip there. He quickly sought to put down that speculation.

In the op-ed piece, Obama said he would send at least two more combat brigades to Afghanistan while leaving "a residual force in Iraq" to chase Al Qaeda remnants, protect U.S. diplomats and remaining forces there and continue training Iraqi security forces.

Obama also promised to commit $2 billion in Iraq refugee support while pursuing "a diplomatic offensive with every nation in the region on behalf of Iraq's stability."

On Monday, some of Graham's heaviest criticism of Obama was reserved for the Illinois senator's claim that "Iraq is not the central front in the war on terrorism, and it never has been." Graham said that Usama bin Laden in 2004 made direct call to sympathizers between the Tigris and the Euphrates, showing that Iraq is a central front to the War on Terror.

Graham also said the surge has been pivotal to gains in Iraq.

"The stunning improvement in security is in direct result of the surge, more combat power, and the model of withdrawing troops to bring about stability and security would have been a disaster," Graham said. "We've got a ways to go yet, but we've turned the corner. And if we start to pull out one to two brigades a month and announce it now, it could jeopardize all the gains that we have made. It would reset the clock in Iraq."

The McCain campaign also issued a number of other comparisons it said showed Obama's continually shifting positions. The release pointed to changing reasons for opposing the surge, and Obama's lack of holding hearings as a subcommittee chairman on Afghanistan or visiting Afghanistan while saying he's concerned about the Central Asian country.

"For now, we'd settle for Obama answering just one question: If he has no intention of listening to what American commanders in Iraq have to say, or incorporating that information into his policy, why is he even going?" McCain spokesman Tucker Bounds said.

McCain's campaign said the Arizona senator will be speaking about his plan for Afghanistan on Thursday. His advisers declined to say whether he agreed with Obama's Afghanistan proposal before the speech.

Obama will be delivering his own speech on Iraq on Tuesday. He has said he is planning on going to that country and Afghanistan with Sens. Chuck Hagel, R-Neb., and Jack Reed, D-R.I., later this month.

U.S. commanders have said they need up to three more brigades in Afghanistan -- or as many as 10,000 additional troops -- to both train Afghan forces and battle the insurgency. President Bush and Defense Secretary Robert Gates have promised to beef up the U.S. force in Afghanistan next year, but military leaders have made it clear they won't be able to do that until they can reduce forces in Iraq.

Currently 36,000 U.S. forces are in Afghanistan, including 17,500 serving with the NATO-led coalition and another 18,500 conducting training and counterinsurgency. Officials said the recent spike in U.S. troops there is the result of the overlap from brigade moving into the country as another was preparing to leave

Violence is on the rise in Afghanistan. Monthly death tolls of U.S. and NATO troops in Afghanistan surpassed U.S. military deaths in Iraq in May and June, and a militant attack Sunday on a remote military outpost killed nine American soldiers, the deadliest assault on U.S. forces in Afghanistan in three years.

FOX News' Jake Gibson and The Associated Press contributed to this report.