"I want to keep my focus on helping find a responsible way out of this tragedy," Hagel said of the Iraq war.
According to a new CBS News/New York Times poll, 75 percent of Americans have not heard enough about Hagel to form an opinion. Six percent said they did not view Hagel favorably, while 4 percent did.
Among Republican primary voters, the numbers are similar, with 76 percent saying they don't know enough about Hagel to form an opinion.
Hagel is probably best known to voters as a high-profile critic of the Bush administration, which dates back to the 2003 invasion of Iraq.
That criticism evolved into heated discordance in January when the Nebraska Republican called President Bush's plan to send an additional 21,500 U.S. troops to Iraq "the most dangerous foreign policy blunder carried out since Vietnam."
Within a week, Hagel helped craft a resolution opposing the plan with two Democrats, Senators Carl Levin of Michigan and Joseph Biden of Delaware. A week after that, Hagel accused the Bush administration of playing "a pingpong game with American lives."
Hagel's rhetoric drew the public ire of Vice President Dick Cheney, who told Newsweek in January that following Republican icon Ronald Reagan's mantra not to speak ill of another Republican is sometimes hard to follow "where Chuck Hagel is involved."
There has been speculation in political circles for more than a year that he might seek the Republican nomination for president in 2008. Hagel has said for weeks that he would make an announcement about his future "soon" but hasn't indicated whether that announcement would reveal his presidential aspirations, if any, or whether he would seek re-election to the Senate in 2008.
Now he's joined the "wait-and-see club," which allows possible candidates to leave the door open, CBS News correspondent Gloria Borger reports. At this early stage in the race, a few candidates, mostly in the Republican party, figure they have nothing to lose by waiting.
Former Republican Sen. Fred Thompson is another.
"I want to see how my colleagues on the campaign trail do, what they say, what they emphasize," Thompson told Fox News.
Hagel, 60, is scheduled to appear with nine declared presidential hopefuls at the International Association of Fire Fighters' annual meeting next Wednesday. Each participant in the bipartisan forum will have 30 minutes to discuss why he or she should be the next president.
Hagel has been the most outspoken Republican critic of Mr. Bush's policy.
"We can't change the outcome of Iraq by putting American troops in the middle of a civil war," Hagel said last month.
If Hagel decides to run for president, he'll be joining an already crowded field of Republican candidates which includes: U.S. Sen. John McCain, R-Ariz., former Massachusetts governor Mitt Romney, former New York City Mayor Rudy Giuliani, Sen. Sam Brownback of Kansas.
That number could grow as former Republican politicians Newt Gingrich and Fred Thompson weigh possible bids.
Hagel's staunch opposition to the administration's Iraq policy is shaped in part by his experience as an Army sergeant in Vietnam, where he served side-by-side with his brother Tom. He was twice wounded in 1968, one of the bloodiest years of the war, earning two Purple Hearts.