Bombing kills at least 43 in Karbala

But noting the fragility of the security gains, Cheney warned against large drawdowns of American troops, saying it is very important that "we not quit before the job is done."

McCain, the presumptive Republican presidential nominee who has linked his political future to military success in Iraq, also promised to uphold a long-term military commitment to the country so long as al-Qaida in Iraq is not defeated.

Both men met in back-to-back meetings with Shiite Prime Minister Nouri al-Maliki, whose government has been accused of failing to make sufficient political progress.

Al-Maliki said he and the vice president discussed ongoing negotiations over a long-term security agreement between the two countries that would replace the U.N. mandate for foreign troops set to expire at the end of the year.

"This visit is very important. It is about the nature of the relations between the two countries, the future of those relations and the agreement in this respect," the prime minister told reporters. "We also discussed the security in Iraq, the development of the economy and reconstruction and terrorism."

McCain: al-Qaida 'not defeated'
McCain stressed it was important to maintain the U.S. commitment in Iraq, where a U.S.-Iraq operation is under way to clear al-Qaida in Iraq from what the military says is the terror group's last urban stronghold of Mosul, 225 miles northwest of Baghdad.

"We recognize that al-Qaida is on the run, but they are not defeated," McCain said after meeting al-Maliki. "Al-Qaida continues to pose a great threat to the security and very existence of Iraq as a democracy. So we know there's still a lot more of work to be done."

McCain, who arrived in Iraq on Sunday, told reporters that he also discussed with the Shiite leader the need for progress on political reforms, including laws on holding provincial elections and the equitable distribution of Iraq's oil riches.

Sen. Carl Levin, D-Mich., speaking to reporters from Kuwait after a visit to Iraq, said Iraq should begin picking up more of the bills.

"We're paying for things that Iraqis clearly should be paying for," Levin said. "They have the capability, the surplus funds to do their own reconstruction, and to do their own weapons purchases and other things which we're paying for and they need to pay for."

Neighborhood security units set up by mainly Sunni Arab tribal leaders and a cease-fire ordered by anti-U.S. Shiite cleric Muqtada al-Sadr for his Mehdi Army militia have also contributed to bringing down violence in recent months, the U.S. military says.

Poll: Most Iraqis feel better off
A poll of 2,000 people from across Iraq, commissioned by international broadcasters including the BBC and ABC, found that 55 percent believe their lives are now better.

But violence is still a daily threat despite security gains.

Roadside bombs and a minibus packed with explosives killed four people, including a policeman, and wounded 13 others in four attacks across Baghdad, police said Monday. Neither Cheney nor McCain were in the area at the time.

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