He earlier told American troops stationed at a sprawling air base north of Baghdad that the United States would fight on in Iraq as the war approaches its fifth anniversary, after warning against large troop cuts.

Wrapping up a surprise two-day trip to Iraq, Cheney met Kurdistan regional president Massoud Barzani, who pledged Kurds would be part of the "solution, not the problem" in the troubled nation's relations with its neighbours.

His visit has been focused on fostering efforts to bring about national reconciliation and defuse the insurgency and sectarian violence that continues to plague Iraq despite a US troop surge.

"We are certainly counting on President Barzani's leadership to help us conclude a new strategic relationship between the United States and Iraq as well as advance crucial peaces of national legislation in the months ahead," Cheney said before heading off to Oman on the next leg of his Middle East tour.

Their talks had also been expected to focus on Turkish operations against Kurdistan Workers' Party (PKK) rebels holed up in northern Iraq, following a major air and ground offensive by Turkey earlier this month.

"We will continue to play our positive role, to be part of the solution, and not part of the problem," Barzani said through an interpreter.

"We will be part of the solution for all the efforts inside of Iraq and out for the neighbouring countries."

Last month's Turkish incursion was branded by Iraqi Kurds and the Baghdad government as an attack on the nation's sovereignty but much of the international community considers the PKK a terrorist group and Washington is believed to back Turkey's strikes.

Cheney said the United States and Iraq's Kurds had built up a "special friendship" during an operation that created no-fly zones over Kurdish areas after the 1991 Gulf War to protect them from ousted dictator Saddam Hussein's brutal campaigns of repression and gas attacks.

At the Balad air base north of Baghdad, Cheney -- a key architect of the invasion unleashed on March 20, 2003 -- vowed to stay the course in Iraq, with the war likely to shape the November US elections.

"They (Iraqis) know we're a nation that accepts a hard job and keeps at it even if others may tire of the effort," he told the troops.

A Cheney aide said he was referring to opposition to the vastly unpopular war at home, not to US allies like Australia who took part in the 2003 invasion but have since withdrawn forces.

The vice president's visit has been marked by a series of attacks, including a bombing near a Shiite shrine in the city of Karbala on Monday that killed 52 people.

On Tuesday, insurgents killed at least seven people in attacks across the country, including two policemen in Baghdad, security officials said.

The Balad base, where Cheney slept on Monday, also reverberated overnight from the thunder of US mortars and artillery being fired into insurgent areas just a few miles (kilometres) away.

Cheney took aim at US opposition to the war, amid renewed calls by Democrats to withdraw the roughly 158,000 US soldiers in Iraq.

"Understanding all the dangers of this new era, we have no intention of abandoning our friends, or allowing this country of 170,000 square miles to become a staging area for further attacks against Americans," he said.

"Tyranny in Iraq was worth defeating. Democracy in Iraq is worth defending. and all Americans can be certain: We intend to complete the mission, so that another generation of Americans doesn't have to come back here and do it again."

On Monday, Cheney urged Arab states to open full diplomatic ties with Iraq if they want to counter the influence of US archfoe Iran, which US commanders accuse of fomenting the violence.

He also criss-crossed the strife-torn capital under heavy guard to assure Iraqi leaders of "unwavering" US support.

Cheney said he saw "phenomenal" and "dramatic" security improvements since his last visit in May 2007, mid-way through a "surge" that saw an additional 30,000 personnel deployed to Iraq.

"It would be a mistake now to be so eager to draw down the force that we risk putting the outcome in jeopardy. And I don't think we'll do that," he said.