A day before the fifth anniversary of the 9/11 attacks, Cheney told NBC television's Meet The Press on Sunday that there have been no al-Qaeda attacks on US soil since September 11, 2001, "We've done a helluva job here at home in terms of homeland security.
"I don't know how you can explain five years of no attacks, five years of successful disruption of attacks, five years of defeating the efforts of al-Qaeda to come back and kill more Americans.
"You have got to give some credence to the notion that maybe somebody did something right," he said.
Cheney said the US had done a good job on "homeland security, in terms of the terrorist surveillance programme we put in place, the financial tracking we put in place, and because of our detainee policy".
Cheney also strongly defended the decision by the government of George Bush, the president, to invade Iraq in 2003.
The invasion was "absolutely the right thing to do," he said. "Because if we weren't there, if Saddam Hussein were still in power, the situation would be far worse than it is today."
Cheney admitted the situation in Iraq is "difficult," but said that without the invasion, Saddam would have posed a significant threat to the US.
"He would be sitting on top of a pile of cash" from high oil prices, Cheney said.
"He would be a major state sponsor of terror. To suggest, somehow, that the world is not better off by having Saddam Hussein in jail, I think, is just dead wrong."
Resistance surprised Cheney
Cheney however said that the strength of the Iraqi fighters had taken the US government by surprise.
"I think that there is no question that the insurgency has gone on longer and been more difficult than I expected," he said.
"The battle against Saddam Hussein and his forces was over in a relatively short period of time. What obviously has developed is the insurgency [which] has been long and bloody.
But Cheney also said that 2005 would be seen as a turning point, in the war.
"That's the point at which the Iraqis stepped up, established their own political process, wrote a constitution, held three national elections and basically took on the responsibility for their own fate and future," he said.
Rice backs Cheney
In a separate interview with CNN on Sunday, Condoleezza Rice, the US secretary of state, said that the US might yet uncover evidence of links between Saddam Hussein and al-Qaeda.
"There were ties between Iraq and al-Qaeda," she said.
"Are we learning more now that we have access to people like Saddam Hussein's intelligence services? Of course we're going to learn more."
A Senate report released on Friday disclosed for the first time that a CIA assessment in October 2005 said Saddam's government "did not have a relationship, harbour or turn a blind eye toward" al-Qaeda operative Abu Musab al-Zarqawi or his associates.
Al-Zarqawi was based in Iraq prior to the 2003 US invasion - but in Kurdistan, an autonomous region outside the direct control of Saddam's government.
Opposition Democrat politicians have argued that the Iraq war has wasted billions of dollars which could have been used to improve domestic security.
Howard Dean, chairman of the Democratic National Committee, said Bush had sought to use the anniversary of the attacks for political gain ahead of November's mid-term elections.
"We think the president has played too much politics. They think they can't win the elections unless they talk about terrorism all the time," Dean said.
Dean said the administration had got bogged down in Iraq when it should have been going "full-scale" after Osama bin Laden.