(Reuters) - Former U.S. Secretary of State Colin Powell on Thursday endorsed Barack Obama's bid for re-election, citing the Democratic president's efforts to wind down the war in Afghanistan and tackle terrorism as well as an improving U.S. economy.

"I think we ought to keep on the track that we are on," the Republican, who also backed Obama in 2008, told "CBS This Morning." He added, "I voted for him in 2008 and I plan to stick with him in 2012."

The move comes just days after Obama and Republican challenger Mitt Romney clashed over foreign policy in the third and last presidential debate ahead of the November 6 election.

Polls show Obama and Romney neck and neck. A Reuters/Ipsos online tracking poll gave Romney a 1-point edge on Wednesday, 47 percent to Obama's 46 percent.

Obama welcomed the endorsement at a rally in Richmond, Virginia.

"I was proud and humbled to learn that we have Colin Powell's support in this campaign. I'm grateful to him for his lifetime of service to his country both as a soldier and as a diplomat," he told the crowd.

The president earlier called Powell to thank him, White House spokesman Jay Carney told reporters aboard Air Force One before landing in Virginia, a battleground state where the military vote is important.

In his endorsement, Powell said domestic issues such as the economy, healthcare and education loomed large in his support for a second term for Obama.

"When he took over, the country was in very, very difficult straits, we were in one of the worst recessions we had seen in recent times, close to a depression ... we were in real trouble," Powell said, adding that housing market has started to pick up, the auto industry has recovered and consumer confidence is rising.

"I think generally we've come out of the dive and starting to gain altitude," he said. "I see that we are starting to rise up," he said, but added problems such as unemployment and the housing market still need work.

Powell also criticized Romney's foreign policy as inconsistent and questioned the former Massachusetts governor's ability to address the deficit and looming defense cuts.

"I'm not quite sure which Governor Romney we'd be getting with respect to foreign policy," he told CBS, calling Romney's foreign policy "a moving target."

As for the U.S. budget, he added: "It's essentially, let's cut taxes and compensate for that with other things, but that compensation does not cover all the cuts intended or the expenses associated with defense."

Powell, a moderate Republican, served as secretary of state under President George W. Bush. Some of Romney's advisers are more conservative veterans of the Bush administration.

"There's some very, very strong neo-conservative views that are presented by the governor that I have some trouble with," Powell said.

A retired four-star general, Powell was also chairman of the Joint Chiefs of Staff under former President George H.W. Bush and was national security advisor under former President Ronald Reagan.

Republican Senator John McCain, a harsh critic of the Obama administration's handling of the wars in Iraq and Afghanistan, blasted Powell's endorsement.

"General Powell, you disappoint us, and you have harmed your legacy even further by defending what has clearly been the most feckless foreign policy in my lifetime," McCain, the Republican presidential candidate who lost to Obama in 2008, told FOX News Radio's "Kilmeade & Friends" program.