Defence secretary conveys US message as Iraqi PM rejects pressure and timetables.
The operation was still in its opening stages, the military said.
Operation Arrowhead Ripper, the New York Times said on Tuesday, was unusual in its scope and ambition, representing a more aggressive strategy of attacking several armed Sunni strongholds simultaneously.
The US daily quoted military officials as saying that Diyala was now home to as many as 2,000 fighters who had flocked there from Anbar, Mosul and Baghdad.
“Let the people of Iraq vote if they want the US to stay or leave”
US commanders say the Baquba fighters are a mix of former members of Saddam Hussein’s army and paramilitary forces, criminal gangs and al-Qaeda members, who are increasingly well trained and highly disciplined.
The New York Times quoted US commanders as saying that the goal was to break the cycle of sectarian killings and retribution that has swept Iraq.
Diyala has emerged as the hotbed of the Sunni Arab anti-government campaign, with al-Qaeda in Iraq and other groups making it their main base of operations.
Violence in Anbar, the original centre of these groups, has dropped after Sunni Arab tribes joined forces with the Americans to drive out al-Qaeda in Iraq fighters.
US security partnership
In related news, Hoshyar Zebari, Iraq’s foreign minister, has said that Baghdad is interested in a long-term security parnership with Washington but has yet to decide if that means US troops will be permanently based in the country.
Speaking to Al Jazeera in Washington DC, where he is to meet Robert Gates, the defence secretary, and other US officials, Zebari said: “The current level of forces, the current strategy, really may not be sustainable in the long term.
“So we are thinking beyond that to seek some arrangements along security partnership arrangement between the Iraqi government and the United States for protection.
“But not to organise that in a sense that their would be permanent bases – still we haven’t reached that.”
On Monday, Iraqi special forces, backed by British troops, killed at least 20 fighters in a series of raids in southern Iraq.
Major David Gell, British military spokesman
The raids were in the Shia city of Amara, 320km southeast of Baghdad, and the nearby town of Majjar al-Kabir, both in Maysan province.
The troops were conducting house-to-house searches at about 2am (2200GMT), Iraqi police and hospital officials said.
Latif al-Tamimi, chief of the security committee on the Maysan council, called the operation a “catastrophe”, accusing troops of firing randomly.
Auda al-Baharani, an al-Sadr spokesman in Amara, said: “The British forces carried out a mission using helicopters and aircraft in Amara. They used bombs, missiles and small arms fire.”