The debate initially focused on Iraq

Republican incumbent Dick Cheney said invading Iraq was "exactly the right thing to do".

Democratic challenger John Edwards accused the administration of "not being straight" with the US people.

The contest is seen as crucial after the perceived win of Democrat John Kerry in the first debate last week.

Opinion polls suggest that Mr Kerry and President George W Bush are running neck and neck ahead of the November election.

What we did in Iraq was exactly the right thing to do Dick Cheney You are still not being straight with the American people John Edwards Debate: Key quotes Full debate transcript (167K) Watch full debate

At the start of Tuesday's debate in Cleveland, Ohio, Mr Cheney - who is seen as an architect of the decision to oust Saddam Hussein - defended President Bush's policy on Iraq.

He added that the former Iraqi leader had "an established relationship" with Osama bin Laden's al-Qaeda network.

Mr Edwards countered by saying that the connection between the two was "tenuous at best".

'Wrong side'

The war, Mr Edwards said, had been a "distraction" from the fight against terror, and accused the administration of having "no plan to win the peace" in Iraq.

Mr Edwards also challenged his opponent over the multi-billion-dollar post-war contracts awarded to Halliburton, the firm Mr Cheney once ran.

Mr Cheney denied any wrongdoing and said the allegations were aimed at obscuring the "undistinguished" record of the Democratic candidates on foreign policy.

HAVE YOUR SAY I have great respect for Cheney, but he was like an old warrior being out boxed by a younger fighter Phil Hawkes, Penticton, Canada Send us your comments

He said Mr Kerry had been "on the wrong side of defence issues" throughout his 30-year political career.

The two men also clashed on the current situation in Afghanistan.

Mr Cheney said the upcoming elections showed that the country had seen "enormous progress" since the US invasion that ousted the Taleban regime in 2001.

Mr Edwards said insecurity in Afghanistan was still rife and most of the country was in the hands of warlords.

In the latter part of the 90-minute debate, the candidates clashed over the economy, health, and other domestic issues.

Mr Cheney accused the Democrats of seeking to raise taxes. Mr Edwards said the Republicans had only cut taxes for millionaires.

Opinion shift

The BBC's Rob Watson in Cleveland says the debate was by and large a more testy affair than the first clash between the presidential candidates.

Opinion poll tracker

What is not clear yet, our correspondent adds, is whether it will prove to be as significant.

During their debate on Thursday, Mr Kerry was seen to score points over Mr Bush when they addressed the violence in Iraq.

Correspondents say the confrontation had a clear impact on voters, with Mr Kerry rising in people's estimation.

The latest opinion poll by CBS News and the New York Times put Mr Kerry and Mr Bush equal with 47% support each.

The findings showed a five-point boost for Mr Kerry after the first debate and erased a month-long Republican lead.

In three key areas for voters - protecting the US from terrorism, ability to handle an international crisis, and having strong qualities of leadership - Mr Bush still led Mr Kerry.

But Mr Kerry increased his standing in all three areas after the debate, the survey indicated.