BAGHDAD — U.S. Vice President Joe Biden arrived in Iraq on Thursday to visit U.S. soldiers, just two days after all American combat troops withdrew from Baghdad and all of Iraq's cities and towns.

During his visit, Biden will meet with Iraqi leaders, including President Jalal Talabani and Prime Minister Nouri al-Maliki.

A White House statement said Biden will reiterate the U.S. commitment to carry out President Barack Obama's plan to withdraw combat forces. He also will press Iraqi leaders to make more progress toward political reconciliation. It was his first trip to Iraq as vice president.

Al-Maliki named the day U.S. combat troops withdrew, June 30, as "National Sovereignty Day" and declared it a public holiday.

On that same day, the White House said that Biden will oversee the administration's Iraq policy and work with its government to overcome their political differences and achieve reconciliation.

In Washington, President Barack Obama said that he has always reserved the right to adjust the U.S. troop withdrawal timetable in Iraq based on changing circumstances. But he said he was confident the U.S. will be able to abide by agreements it made with Iraqis.

Biden arrived as violence flared for another day in the Iraqi capital, with bombings killing at least three people in the Baghdad area in the first significant violence since Iraqi forces assumed responsibility for securing cities after the withdrawal of U.S. combat troops from urban areas earlier this week.

Elsewhere, a car bomb near the northern city of Kirkuk killed one man and wounded six more, police said.

In Baghdad, the violence began when a roadside bomb struck an Iraqi army patrol, killing an Iraqi soldier and wounding seven other people, police and hospital officials said.

The attack occurred near a bridge that controls access to the walled-off Green Zone in central Baghdad.

A car bomb later exploded near a market on the highway south of Baghdad, killing at least two people and wounding 15, according to a police officer at the regional command.

The officials spoke on condition of anonymity because they weren't authorized to release the information.

On Tuesday — the official day of the withdrawal — a car bomb killed more than 30 people in the northern city of Kirkuk.

But Thursday's bombings were the first deadly attacks recorded in Baghdad after the Iraqis officially assumed responsibility for securing the cities and most of the 130,000 American troops in Iraq pulled back from urban areas to large bases on the outskirts.

Persistent violence has raised concerns about the readiness of Iraqi forces to take over their own security.