By Ross Colvin

BAGHDAD, July 29 (Reuters) - The U.S. military on Sunday dismissed reports that the top U.S. general in Iraq, General David Petraeus, had a stormy relationship with Iraq's prime minister, but said the pair had "very frank talks".

Tensions have surfaced between Prime Minister Nuri al-Maliki and U.S. officials as he comes under increasing pressure from Washington to speed up passage of legislation seen as crucial to easing violence between the country's Shi'ite and Sunni Arabs.

But a British newspaper reported on Saturday that the situation had got so bad that Maliki had asked U.S. President George W. Bush to remove Petraeus, who is directing Bush's new counter-insurgency strategy.

"This is a totally fabricated story," said Petraeus's spokesman, Colonel Steve Boylan.

"They have very frank, open, and perhaps direct conversations and continue to do so. Based on what is at stake here, that is what is needed and it should be expected that both are able to have very open and frank dialogue," he said.

The Daily Telegraph characterised the relationship between the two as stormy and said they had frequent shouting matches. "I can't deal with you anymore. I will ask for someone else to replace you," Maliki told Petraeus at one meeting, it said.

The newspaper and another media report said at one video teleconference with Bush, Maliki, angry over the U.S. military's alliance with some Sunni Arab tribal groups, had threatened to arm Shi'ite militias.

CROSSED SWORDS

"General Petraeus and others have sat in on every video teleconference with PM Maliki and President Bush. Those statements have never been even hinted at," Boylan said.

A senior adviser to Maliki, Sadiq al-Rikabi, also dismissed the allegations as untrue.

"I asked him personally yesterday whether there was a problem between him and General Petraeus and he told me there were no problems whatsover."

He said there had been tensions over the U.S. military's recruitment of Sunni Arab tribal police to fight al Qaeda but said agreement had since been reached to form an Iraqi government committee to vet the recruits.

A U.S. embassy spokesman said he had no comment on the newspaper report but pointed to an interview given by U.S. ambassador Ryan Crocker this week in which he said:

"There is no leader in the world that is under more pressure than Nuri al-Maliki ... I have great admiration for PM Maliki and I know General Petraeus does as well. I would like to think it is reciprocated."

Maliki has often crossed swords with U.S. commanders over his lack of control over his own security forces, while the commanders have complained that he has repeatedly undermined efforts to rein in Shi'ite militias.

Bush has sent nearly 30,000 extra troops to Iraq to give Maliki's government breathing space to pass laws on control of Iraq's vast oil reserves, setting a date for provincial polls, and easing restrictions on members of Saddam Hussein's Baath party serving in the government and the military.

Despite some military successes, notably in quelling violence in the capital, none of the laws have been passed and Iraq's parliament is due to go on summer recess on Wednesday.

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