BAGHDAD, Iraq – Insurgents killed 39 people in a series of rapid-fire attacks yesterday, including three suicide car bombings within an hour and a drive-by shooting at a busy Baghdad market that ratcheted up the bloody campaign to undermine Iraq’s government.

Iraq’s interior minister, meanwhile, claimed the government offensive seeking to root out rebels in Baghdad had scored big gains, saying this week’s sweep by Iraqi soldiers and police captured 700 suspected insurgents and killed 28 militants.

Iraqi and American forces have stepped up operations to answer an insurgent onslaught that has killed at least 814 people since Prime Minister al-Jaafari announced his Cabinet five weeks ago, but militants staged deadly attacks across a swath of northern Iraq.

In Tuz Khormato, a popular highway stop 55 miles south of the oil-rich town of Kirkuk, a suicide car bomber targeted bodyguards for Iraq’s Kurdish deputy prime minister as they ate at a restaurant. The blast killed 12 people.

“I was sitting inside my restaurant when about six cars parked nearby and their passengers came inside and ordered food,” the owner, Ahmed al-Dawoudi, said. “Seconds later, I heard a big explosion and the restaurant was turned into twisted wreckage and rubble. Blood and pieces of flesh were everywhere.”

Earlier in Kirkuk, a suicide car bomber trying to attack a convoy of civilian contract workers killed a young boy and three other Iraqi bystanders and wounded 11 people.

Another suicide bomber killed four people and wounded four in Baqouba, about 35 miles northeast of Baghdad. Hours later, two parked motorcycles rigged with bombs blew up near a coffee shop there, killing five Iraqis and wounding 13.

In the capital, men in three speeding cars sprayed gunfire into a crowded market in the northern neighborhood of Hurriyah, killing nine people, the interior and defense ministries said. Two other attacks in the Baghdad area killed four people and injured three.

As part of the campaign against insurgents, Iraq’s government launched in Baghdad on Sunday the biggest Iraqi offensive since Saddam Hussein’s fall two years ago.

Officials say 40,000 soldiers and police, supported by American forces, have thrown a cordon around the city of 6 million people in an effort to cut off access. Before the offensive, authorities controlled only eight of Baghdad’s 23 entrances, the interior minister, Bayan Jabr, said.

“By organizing our forces and devising security plans, we will be able in the next few months to significantly reduce terrorism and killings,” Mr. Jabr said.

He said the Baghdad operation had netted at least 700 people he labeled “terrorists” and killed 28 rebels in firefights. In addition, 118 criminal suspects had been arrested, he said.

“We believe the security situation has improved by 60% since Operation Lightning began,” Mr. Jabr said.

Among those captured in Baghdad is the suspected leader of the National Islamic Resistance/1920 Revolution Brigade terror group, the Defense Ministry said.

Angry leaders of the Sunni Arab minority complained yesterday that their community was being targeted by the crackdown and threatened to boycott the drafting of Iraq’s new constitution – a crucial document American officials hope will help stabilize Iraq.

“I swear by God that we’ll demand none from now on to lay down his weapon,” yelled Osam Al-Rawi, head of the Iraqi teachers union and representative of the influential Association of Muslim Scholars, a Sunni group thought to be close to the insurgency.

However, in a heartening sign, Sunni leaders did not slam the door on Mr. al-Jaafari’s efforts to bring them back into the political fold.

Members of the constitutional committee met with about 70 Sunnis, including members of the Iraqi Islamic Party and the Association of Muslim Scholars, to discuss parliament’s offer for 13 Sunnis to represent the minority on the 55-member charter panel. Just two Sunni Arabs are on the body now. Abdul-Hamid said that despite his anger, he was not rejecting the political process.

“We all are convinced, whether the government, occupation forces, or political parties, that channels should be opened with the Iraqi Islamic national resistance, which defends Iraq and its independence,” he said, adding it was “very useful to reach out and find solutions for ending the occupation and stop the blood letting.”

In other developments yesterday:

* A senior member of the Shiite Badr Brigade militia, Sheik Safwan Ali Farhan, died after being shot Monday in eastern Baghdad, police said.

* The American military said two American soldiers were killed in combat near Ramadi and another died of non-battle injuries in Kirkuk on Wednesday. At least 1,666 American military members have died since the war began in March 2003, according to an Associated Press count.