U.S. Vice President Dick Cheney paid a visit to Baghdad just before the five-year anniversary of the U.S.-led invasion of Iraq. The vice president hailed progress in Iraq and promised continued support from Washington. Meanwhile, a female suicide bomber has killed 40 people and wounded more than 70 near a Shi'ite shrine in Karbala. Daniel Schearf reports from the northern Iraqi city of Irbil

Vice President Cheney arrived in Baghdad for meetings with Iraqi officials.

Cheney met with Iraq's Prime Minister Nouri al-Maliki. The two discussed the situation in Iraq, regional security, and bilateral relations.

The vice president was a key architect of the U.S.-led invasion of Iraq. He said his visit was to send President Bush's thanks and to reaffirm an "unwavering commitment" from the U.S. to Iraq's future.

"It is especially significant, I think, to be able to return this week as we mark the fifth anniversary of the beginning of the campaign that liberated the people of Iraq from Saddam Hussein's tyranny and launched them on the difficult but historic road to democracy," he said.

Tens of thousands of Iraqis and more than 4,000 U.S.-led coalition troops have died since the 2003 overthrow of Saddam Hussein in ongoing violence across the country.

But Mr. Cheney said since his last visit 10 months ago he saw phenomenal changes in Iraq in security and political developments.

The U.S. military says violent attacks have dropped by 60 percent since June.

Also, Iraq this year passed several long-delayed laws seen as important for fostering trust between Iraq's Shiites, Sunnis, and various ethnic groups, as well as the central and local governments.

But other laws seen as important in that regard, one on provincial elections and another on sharing oil revenues, have yet to be passed.

Mr. Maliki said the two leaders also discussed negotiations over future diplomatic and military relations. He thanked the vice president for U.S. recognition and support of Iraq's achievements. He says the frequency of these visits by the vice president are very important and that they cement and support the relationship between the two countries and the success that they have achieved in Iraq in the global war against terrorism. He says it is very important to have these meetings and these successes.

Cheney's surprise visit coincided with one by presidential candidate and U.S. Senator, John McCain, who arrived Sunday. McCain is in Iraq to assess the recent security gains, which are still considered fragile.

A series of deadly suicide bombings this year drove up the death toll and reversed six-months of falling casualty figures. But, the U.S. military says it does not yet indicate a new trend.

As the U.S. leaders were in Baghdad, bombs in the capital killed at least four people, including a policeman, and wounded several others.

Explosions were also heard near the "Green Zone," the heavy security area that houses the Iraqi government and the U.S. Embassy. But, it is not clear if anyone was injured.