America cannot "dictate to the world" and must work with allies and build relationships with other nations, US Defense Secretary Chuck Hagel said shortly after being sworn in Wednesday as the new Pentagon chief.

On his first day at the job, Hagel reinforced his reputation as a reluctant warrior as he told an auditorium of civilian officials and military officers that America was a powerful country but could not accomplish its goals without forging strong alliances.

"I've always believed that America's role in the world ... has been one that should engage the world. We can't dictate to the world. But we must engage in the world," Hagel said.

"No nation, as great as America is, can do this on their own. We need to continue to build on the strong relationships that we have built."

Defense secretaries often adopt a tough tone to signal resolve to America's adversaries, but Hagel's comments echoed President Barack Obama's emphasis on extricating the country from a decade of ground wars in Iraq and Afghanistan.

US troops have pulled out of Iraq in 2011 and roughly 66,000 American forces are due to withdraw from Afghanistan by the end of 2014, a drawdown that Hagel will be charged with overseeing.

Hagel told the Pentagon audience that the United States was ultimately a force "for good" but had a duty to exercise its power with care.

"We make mistakes. We've made mistakes. We'll continue to make mistakes. But we are a force for good," he said.

Hagel, an outspoken opponent of the Iraq war during George W. Bush's presidency, added that "we have great power, and how we apply our power is particularly important.

"That engagement in the world should be done wisely."

Hagel, 66, took his oath of office at about 8:30 am (1330 GMT) at the Pentagon as his wife looked on, becoming the first combat veteran from the Vietnam conflict to take up the post.

In his remarks to Pentagon employees, Hagel spoke without notes and struck an upbeat tone despite a nasty debate in the Senate over his nomination that saw him struggle to win enough votes for confirmation.

Despite the bitter atmosphere that prevailed at his confirmation hearing, in which he was pummeled by his former Republican colleagues over his statements on Iran and Israel, officials said Hagel would seek to cooperate with Congress.

"Senator Hagel has signaled his very strong commitment right away to get down to business, to get deeply invested in the work of the Pentagon and its military and civilian workers," Pentagon spokesman George Little told reporters Tuesday.

"His goal is to look to the future."

Although Hagel's opponents failed in the end to derail his nomination, their hostile stance signaled that the former infantryman would have little breathing room when it comes to working with Congress, without the kind of bipartisan support some of his predecessors enjoyed.

After a bruising Senate confirmation hearing and a 10-day delay engineered by Republicans, senators voted 58-41 to approve Hagel on Tuesday. But in 2011, senators approved his predecessor, Leon Panetta, for the job by a unanimous vote.

Within 48 hours after being sworn in, Hagel will confront steep automatic cuts to the Pentagon's budget of roughly $46 billion which are due to kick in Friday amid political deadlock in Congress.

He also will have to grapple with a major troop withdrawal from Afghanistan, renewed threats posed by a defiant North Korea and turmoil in the Middle East.

Hagel's searing experience in the jungles of Vietnam has shaped his cautious view of military power, and he has often said war should be a last resort only after diplomacy has been exhausted.

In Vietnam, Hagel served with his brother as an infantry squad leader and saw combat first-hand in the Mekong Delta, earning two Purple Hearts after suffering shrapnel wounds to his chest and burns to his face.

He still has some shrapnel fragments lodged in his chest.