In the northern city of Mosul, a roadside bomb ripped through an Iraqi army patrol soon after sundown, killing three soldiers and wounding four others, police said.
U.S. and Iraqi troops have been fighting for months to clear al Qaeda in Iraq and about a dozen other Sunni insurgent groups from Mosul, Iraq's third largest city.
To the south, a bomb attached to a bike wrapped in a trash bag exploded outside a cafe in Khalis, 50 miles north of Baghdad, killing at least two people and wounding 13, including the city mayor, police said.
The cafe is located in a market area that includes a public health clinic and the precise target was unclear. Khalis is a mostly Shiite town surrounded by Sunni communities and was a hotbed of Sunni-Shiite fighting in 2006 and 2007.
In Anbar province, a woman suicide bomber blew herself up at a hospital in Amiriyat al-Fallujah, a suburb of Fallujah, about 40 miles west of the capital.
Talib al-Hassnawi, a member in Fallujah municipal council, said three people were killed and five were wounded.
Police said the dead included two women and a 10-year-old girl.
All the policemen spoke on condition of anonymity because they were not supposed to release the information.
A car bomb was discovered Sunday behind the governor's office in the northern oil city of Kirkuk. Police became suspicious and summoned U.S. troops who cleared the area and detonated the vehicle without casualties, police Col. Taha Salahuddin said.
Four men were arrested, he added.
In Baghdad, six people, including three policemen, were wounded by a roadside bomb in the eastern part of the city, the U.S. military said.
The attack in Amiriyat al-Fallujah occurred one day after a suicide bombing killed eight people and wounded 17 at a police checkpoint near Ramadi, about 25 miles to the west.
The violence comes two months after the U.S. handed control of Anbar province over to the Iraqis and shows that militants have still not given up the fight despite setbacks at the hands of U.S. and Iraqi forces.
The attacks occurred as Prime Minister Nouri al-Maliki is studying the U.S. response to the government's request for changes in a draft security agreement that would keep U.S. troops in the country until the end of 2011.
Iraq's parliament must approve the deal by the end of the year when the U.N. mandate under which U.S. forces operate here expires. Without an agreement or a new mandate, most all military operations will cease.
The draft agreement that has drawn sharp criticism from Iraqi Shiite clerics and Shiite-dominated Iran. Tehran's closest Arab ally, Syria, lashed out against the pact Sunday.
Assad pointed to a recent American cross-border raid into Syria as evidence that the U.S. will use Iraq as a base to attack its neighbors.
"The latest American aggression on Syrian territory shows that the presence of American occupation forces constitutes a source of continuous threat to the security of Iraq's neighboring states and a factor of instability for the region," he said.
The U.S. has accused both Iran and Syria of supporting Iraqi insurgents - charges both countries deny.
Iraq has asked the U.S. for an explicit ban in the proposed security pact on the use of Iraqi soil for attacks against the country's neighbors.
Also Sunday, the Cabinet held a special session to discuss a reduction in the 2009 national budget to take into account sharp falls in oil prices.
Iraqi authorities set the original draft budget last month at around $80 billion, based on expectations that the average price per barrel of oil would not drop below $80. Oil was trading Friday at about $61 a barrel on the New York Mercantile Exchange.
The Finance Ministry has proposed a revised 2009 budget of 79 trillion Iraqi dinars ($68.7 billion), government spokesman Ali al-Dabbagh said. He said the ministry estimated a new average price of oil during the coming year of $62.5 per barrel.
By Associated Press Writer Sameer N. Yacoub; AP writers Sinan Salaheddin in Baghdad and Albert Aji in Damascus, Syria contributed to this report