(Adds other attacks south of Baghdad)

KERBALA, Iraq, Aug 27 (Reuters) - Police killed three people on Monday night in clashes with pilgrims in Iraq's city of Kerbala, where tens of thousands of Shi'ites have gathered for one of the holiest days on the Shi'ite calendar.

A Reuters photographer said he saw one pilgrim shot dead outside his hotel. Several wounded people were carried away by fellow pilgrims.

A water tanker was ablaze and the sounds of gunfire echoed in the streets around the hotel, situated between the Imam Hussein and Imam Abbas mosques, for about two hours, he said.

Police said they opened fire on a large crowd of pilgrims infuriated by the strict security measures in force in the city for the celebrations, killing three and wounding 13. The shots were fired after the pilgrims began brawling with the policemen.

A pilgrim in Kerbala said tensions were running high in the city. He said that scores of policemen were on the main roads leading to the two shrines and others on rooftops. Some carried heavy machineguns and rocket-propelled grenade launchers.

In the towns of Iskandariya and Latifiya, south of Baghdad, Police said gunmen killed one pilgrim and wounded five.

And in Falluja, a town west of Baghdad, a suicide bomber killed 10 people and wounded 11 when he blew himself up after evening prayers in a mosque, police and hospital sources said.

The surge in violence came as the United States was pushing for a political accord between Iraqi leaders to reduce sectarian violence that has killed tens of thousands of Iraqis.

Some 10,000 police officers and 5,000 Iraqi soldiers had been deployed in Kerbala ahead of a ceremony on Tuesday and Wednesday marking the 9th century birth of Muhammad al-Mahdi.

Shi'ites believe Mahdi, the last of 12 imams they revere as saints, never died and will return to save mankind.

Pilgrims from Baghdad and other Shi'ite towns have been converging on Kerbala, mostly on foot, in the past few days.

Shi'ite pilgrimages have been a target of Sunni bombers and have also served as rallying events for the Shi'ite majority, now running Iraq after decades under Saddam Hussein.

The pilgrimage had so far been largely peaceful, with few reports of any violence.

ACCORD QUESTIONED

Earlier on Monday, a Sunni leader said that a new political accord between Iraq's main leaders would not be enough to lure minority Sunni Arabs back into the government.

Five political leaders announced the deal late on Sunday, agreeing measures to readmit former members of Saddam's Baath Party to public life and the release of many detainees.

"What happened yesterday is a good achievement in the current confused political situation. It is an achievement that deserves to be supported," Tareq al-Hashemi, the Sunni Arab vice president who signed the accord, told reporters.

Hashemi, of the Sunni Accordance Front, signed the deal along with Prime Minister Nuri al-Maliki, a Shi'ite, and three other leading Shi'ite and Kurdish political leaders.

But he said the Front, which groups three parties, would not change its Aug. 1 decision to quit the cabinet.

"Our previous experience with the government has not been encouraging, and we will not go back just because of promises, unless there are real and tangible reforms," he said.

U.S. Ambassador Ryan Crocker hailed the deal, which will give him some good news to deliver in two weeks when he and the top U.S. general in Iraq, David Petraeus, report back to Washington in a pivotal moment for U.S. policy.

"The statement released by the five leaders yesterday is a positive and encouraging message that the government is making all efforts to achieve benefits for Iraqi people," Crocker told a conference in Arabic on Monday.

"I'm optimistic. I can see there is progress," said Crocker. The remarks were a significant change of tone for the diplomat, who said just a week ago that the government's progress was "extremely disappointing".

Experts question whether the five leaders who reached the deal have enough support to pass laws in parliament.

On the Sunni Arab side, Hashemi leads just one of the three parties in the Accordance Front. On the Shi'ite side, the leaders who signed the deal did not include followers of cleric Moqtada al-Sadr, whose ministers quit the government this year.

"I don't see how they can push these through parliament when they don't have a majority in parliament," said Joost Hiltermann of the International Crisis Group think tank.

Political leaders in Iraq have announced broad agreements in the past but struggled to implement them or hammer out details. (Additional reporting by Wisam Mohammed, Ahmed Rasheed and Peter Graff)

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