WASHINGTON (CNN) -- Sen. Barack Obama said Thursday that the most important thing he could achieve as president would be to deal with Iraq and the threat of al Qaeda in Afghanistan while improving "our influence around the world."

Sen. Barack Obama, in his first interview since the North Carolina and Indiana primaries, speaks with Wolf Blitzer.

In his first interview since the North Carolina and Indiana primaries, Obama said he thinks the United States' influence around the world has been diminishing.

"The world wants to see the United States lead. They've been disappointed and disillusioned over the last seven, eight years," he told CNN's Wolf Blitzer in an interview on "The Situation Room."

"I think there is still a sense everywhere I go that if the United States regains its sense of who it is and our values and our ideals, that we will continue to set the tone for a more peaceful and prosperous world." Watch the full interview with Obama »

Obama said he thinks the way the war in Iraq has been handled has kept the United States from focusing on key issues like energy policy, global warming and the economy.

Americans want to succeed, he said, "but we're going to have to make some investments and ensure that the dynamism and the innovation of the American people is released."

"It's very hard for us to do that when we're spending close to $200 billion a year in other countries, rebuilding those countries instead of focusing on making ourselves strong," he said.

Obama downplayed headlines and stories, such as the cover of Time magazine, that have declared him the Democratic presidential nominee.

"I don't want to be jinxed. We've still got some work to do," he said. Watch an analysis of some of Obama's comments »

Obama predicted that he and Sen. Hillary Clinton would probably split the remaining contests and said Clinton would win the upcoming primary in West Virginia by a "big margin."

Obama won North Carolina by a 14-point margin Tuesday. Clinton squeaked out a win in Indiana by 2 points.

In the days after those contests, some top Democrats have called on Clinton to step aside.

Obama deflected a question about a potential joint ticket with the New York senator, saying it's too early to start thinking about running mates.

"Sen. Clinton has shown herself to be an extraordinary candidate. She's tireless, she's smart, she's capable, and so obviously she'd be on anybody's short list to be a potential vice presidential candidate," he said. "But it would be presumptuous of me at this point ... to somehow suggest that she should be my running mate." Watch viewer responses to question: Should Obama offer Clinton the No. 2 spot? »

Terry McAuliffe, a former Democratic National Committee chairman and a co-chairman of Clinton's campaign, commented Thursday on the possibility of a joint ticket.

"I think what she's interested in being the nominee of the party. ... We're fighting hard for it. This woman has been working tirelessly through this campaign. ... Hillary has earned the right to do whatever she wants to do."

Obama said he's ready for what would be the next phase if he becomes the nominee: a matchup against Sen. John McCain, the presumptive GOP candidate.

Obama said he was offended when McCain said last month, "It's very clear who Hamas wants to be the next president."

"I think it's disappointing because John McCain always says, 'Well, I'm not going to run that kind of politics,' and then to engage in that kind of smear I think is unfortunate, particularly since my policy on Hamas has been no different than his," Obama said.

"And so for him to toss out comments like that, I think, is an example of him losing his bearings as he pursues this nomination."

When asked to respond to McCain supporters -- such as former Massachusetts Gov. Mitt Romney -- who have said Obama is not ready to be commander in chief, the senator from Illinois said he thinks what people are looking for is "good judgment."

"I think I've consistently displayed the kind of judgment that the American people are looking for in the next president," he said. Watch Obama say why he's qualified to be president »

Romney responded later on "The Situation Room," saying "The truth of the matter is just as I said, that he doesn't have a record of accomplishments in the private sector or in the governmental sector ... hasn't pushed a major piece of legislation.

"He seems like a charming guy who's very well-spoken. But in terms of actually having led, actually having accomplished something, actually having a kind of leadership that America needs at a critical time with our economy ... he's untested. ... Frankly, Sen. McCain is someone who is tested and very proven," he added.

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