US Secretary of State Condoleezza Rice has said Iraq's leaders are "off to a good start" with a new security plan intended to cut violence.
Explosions occurred in northern Kirkuk at a crowded market
On an unannounced visit to the capital, Baghdad, she said she was "very impressed" with Prime Minister Nouri Maliki's leadership.
Earlier, two car bombs in Kirkuk killed at least 10 people and injured 68.
The blast also destroyed shops at the market, situated in a mainly Kurdish area of the city.
Kirkuk, 290km (180 miles) north of Baghdad, is a centre of oil production and ethnically mixed, with tensions running high between different groups.
The secretary of state's visit comes as the Democratically-controlled US Senate prepares to hold a session on whether to vote on a non-binding resolution criticising the Iraq security plan.
Written by the Democrats, the resolution states that the Senate "will continue to support and protect" US soldiers in Iraq but that it "disapproves" of the 21,500-strong troop increase.
On Friday, the House of Representatives passed an identical resolution, with 17 Republicans joining the Democrats.
Violence in Baghdad itself has reduced by 80% since the new security operation began three days ago, said an Iraqi military spokesman Brigadier Qasim al-Mousawi.
Rice praised Maliki's efforts
"The morgue was receiving 40 to 50 bodies per day before and now has received only 20 in the last 48 hours," he said.
He added that illegal checkpoints had been dismantled and 330 displaced families had been able to return to their homes.
This is rare good news for the US administration which is facing opposition at home to its strategy of sending more troops to Iraq, says the BBC's Jane Peel in Baghdad.
However a senior US military commander has warned that the militants are probably lying low and are likely to be back.
The US secretary of state held talks with Mr Maliki and other senior Iraqi leaders, and said it was important for the Iraqi security forces to consolidate on the lull in the violence.
"We have been reviewing the prospects for the Baghdad Security Plan," said Ms Rice, after the meeting. "This can be a new phase for the people of Iraq."
She said the US was also looking at ways to help Iraq and neighbouring countries cope with the large numbers of refugees escaping the violence:
"I have talked to the prime minister about the importance of making certain that people who are refugees can find shelter," she said.
"But ultimately we hope that a stable Iraq will be a place to which all Iraqis can return."
The secretary of state later went on to Israel for talks on the stalled peace process with the Palestinians.