(Refiles, fixing typo in para )

By Mariam Karouny and Peter Graff

BAGHDAD, Aug 1 (Reuters) - The main Sunni Arab political bloc quit the Iraqi cabinet on Wednesday, plunging the government into crisis on a day when suicide bombers killed more than 70 people with massive strikes in the capital.

The Sunni Accordance Front said its five cabinet members and Deputy Prime Minister Salam al-Zobaie would resign from Prime Minister Nuri al-Maliki's government.

"This is probably the most serious political crisis we have faced since the passage of the constitution. If unresolved the implications are grave," the remaining deputy prime minister, Barhim Salih, a Kurd, told Reuters.

Maliki spoke to U.S. President George W. Bush by video link and reassured him "dialogue with our brothers in the Accordance Front will not stop" despite the boycott, Maliki's office said.

White House spokesman Tony Snow said after the call:

"The president emphasized that the Iraqi people and the American people need to see action, not just words ... on the political front," Snow told reporters in Washington.

The Iraqi government said 1,653 civilians were killed in July, a third more than the previous month, despite a fall in the number of deaths among U.S. troops.

Fifty of Wednesday's dead were killed when a suicide bomber in a fuel truck packed with explosives targeted motorists at a petrol station, police said. Another suicide bomber killed 20 people outside a popular ice cream shop across town. Another bomber killed three in southern Doura district.

The Accordance Front said it was quitting Maliki's coalition because he had failed to meet about a dozen demands, including granting the Sunni bloc a greater say in security matters. Those standing down include the ministers of culture, women, planning, and higher education, and the junior foreign affairs minister.

Their withdrawal may have little practical effect on a government already paralysed by infighting. The Shi'ite bloc of radical cleric Moqtada al-Sadr withdrew in April.

But the withdrawal was a blow to reconciliation efforts: luring the large Sunni bloc into government had been hailed as a major achievement when Maliki took power last year.

The United States had hoped the inclusion of Sunni Arabs in the Shi'ite-dominated government would reduce sectarian violence. But laws aimed at reconciliation have not been passed.

Washington acknowledged the setback. "Democracy is hard," said U.S. embassy spokesman Phil Reeker. "Is it frustrating? Yes. It's frustrating for us, it's frustrating for them, it's frustrating for the Iraqi people."

Haidar al-Ibadi, a parliamentarian close to Maliki, told Reuters the Front was trying to persuade the Americans to withdraw support for the prime minister.

"They are sending a message to Washington that Nuri al-Maliki is no longer accepted, and trying to bring the political process to square one. They will not be successful."

The Sunni Front's deputy president, Tareq al-Hashemi, will remain in office for now, as will Sunni Arab Defence Minister Abdel Qader Jassim. The Front's 44 members also remain in the 275-seat parliament, which is on recess until September.

TALKS PLANNED

Salih, the Kurdish deputy prime minister, told Reuters plans were under way for a summit of Iraq's main factions in the next few days, seeking a new, more stable accord.

"The crisis is grave and its implications should not be underestimated, but I hope it offers an opportunity to address the causes of political instability afflicting this country."

Hashemi told reporters the Front was still open to talks and could return to government "if they introduce reforms".

Political setbacks in Iraq could also hurt Bush, who faces a showdown in Congress next month when his Iraq commander reports on progress after sending 30,000 extra troops this year.

The military reported that four more soldiers had been killed on Tuesday, July's last day, taking the month's toll to 78, the lowest since last November.

"The surge has done what we wanted it to do in terms of bringing down the violence," said the U.S. embassy's Reeker. "The hardest part is taking advantage of these security gains to move the political process forward."

But deaths among Iraqi civilians, which had fallen by more than a third in June, rose back to the level of previous months.

(Additional reporting by Paul Tait, Ross Colvin, Aseel Kami, Wathiq Ibrahim in Baghdad)

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