The bombers struck at about 9:45 a.m., when officers usually stop by the restaurant for breakfast. Police Maj. Falah al-Mohammedawi said 35 officers and civilians died and 25 were wounded.
The blasts came just before British Foreign Secretary Straw was expected in the country for a meeting with Prime Minister Ibrahim al-Jaafari.
Samiya Mohammed, a housewife who lives nearby, said she rushed outside when she heard the explosion.
"I went out to see the restaurant heavily damaged. There was bodies, mostly civilians, and blood everywhere inside the place. This is a criminal act that only targeted and hurt innocent people having their breakfast," she said.
There were no Americans in the area, she said.
"I do not understand why most of the time it is the Iraqis who are killed," she said.
In other developments:
Iraqi soldiers found the bodies of 27 people near the Iranian border Thursday, an Iraqi officer said, adding that they appeared to have been dead for several days.
The victims were bound, shot in the head and wearing civilian clothes when they were found near Jassan, 130 miles southeast of Baghdad, Iraqi Army Col. Ali Mahmoud said. The identities of the victims were not immediately known.
Groups of dead bodies — suspected victims of sectarian death squads — turn up with alarming regularity in Iraq. Officials suspect that death squads from the Shiite majority or the Sunni minority are responsible for the killings.
At least 566 bodies have been found since Iraq's interim government was formed April 28 — 204 in Baghdad — according to an Associated Press count. The identities of many are unknown, but 116 are known to be Sunnis, 43 Shiites and one Kurd. Some are likely victims of crime — including kidnappings — rampant in some cities and as dangerous to Iraqis as political violence.