(Recasts with Bush comments, new Crocker quotes)

By Mariam Karouny

BAGHDAD, July 24 (Reuters) - The United States accused Iran in talks on Tuesday of increasing support for militias involved in bloodshed in Iraq but, in a rare sign of cooperation, agreed with Tehran to set up a panel to improve security.

In their second round of talks on Iraq this year after a long diplomatic freeze, U.S. Ambassador to Iraq Ryan Crocker said he also challenged Iran over its suspected support for other radical groups in the Middle East such as Hamas and Hezbollah. Iran rejected all of the accusations, he said.

"We expressed concerns over Iranian activities and support of violent militia elements through both arming and training," he said after meeting Iranian Ambassador Hassan Kazemi-Qomi.

"The fact is, and we made it very clear in today's talks, that over the roughly two months we have actually seen militia-related activities that can be attributed to Iranian support go up and not down."

Crocker said Iran agreed in principle to join a new trilateral security sub-committee to investigate issues such as support for extremist militias and al Qaeda in Iraq. Details will be worked out in the next few days, he said.

"They maintain they're serious about assisting Iraq to improve security and stability, so the opportunity is in front of them. We'll measure it by actions on the ground," Crocker said, speaking later to reporters by telephone.

U.S. President George W. Bush, faced with a new opinion poll showing anti-war sentiment on the rise, on Tuesday ratcheted up his efforts to link the U.S.-led fight in Iraq to the broader battle against al Qaeda.

Bush cited newly declassified intelligence as he gave an impassioned response to criticism that the U.S. focus on Iraq has become a distraction from the wider war on terrorism.

"Al Qaeda in Iraq is a group founded by foreign terrorists, led largely by foreign terrorists and loyal to a foreign terrorist leader: Osama bin Laden," Bush told an audience at an air force base in Charleston, South Carolina.

SUICIDE ATTACK

In Iraq, a suicide car bomber killed 26 people and wounded 70 on Tuesday in a crowded market near a maternity hospital in the Shi'ite town of Hilla, 100 km (60 miles) south of Baghdad, police said.

Washington has accused Shi'ite Muslim Iran of fomenting violence in Iraq through support for Shi'ite Muslim militias. Iran denies the charges and blames the 2003 U.S.-led invasion for the bloodshed between Iraq's Shi'ite majority and Sunni Arab minority.

The United States and Iran, which have not had diplomatic ties since shortly after Tehran's 1979 Islamic revolution, held what were widely seen as breakthrough talks in Baghdad in May about finding ways to help end the conflict in Iraq.

Tuesday's talks took place less than two months before Crocker and the top U.S. commander in Iraq, Gen. David Petraeus, have to present a crucial report in mid-September to the U.S. Congress on Iraq's political and security progress.

Iraqi Prime Minister Nuri al-Maliki's fractured coalition government is under pressure from Washington to meet political benchmarks designed to promote national reconciliation before Congress receives the progress report.

Crocker said there had been several "heated exchanges" in the seven hours of talks, and Iraqi Foreign Minister Hoshiyar Zebari described them as "very challenging." No immediate comment was available from the Iranian delegation.

Crocker also blamed Iran for an increase in attacks on Baghdad's international zone in recent weeks, saying the "overwhelming majority" of fire came from areas dominated by militia groups known to have connections with Iran.

He added he warned Tehran that operatives with its Quds force, part of its Revolutionary Guard, and their surrogates "are not going to be safe in Iraq".

Earlier, Maliki urged Washington and Tehran to help Baghdad and warned that insurgent groups such as al Qaeda were moving to other countries after they were hit in Iraq.

"We are looking for your support to stabilize Iraq, which does not want to interfere in other countries' business, nor does it want others to interfere in its internal affairs," Maliki said when he opened the meeting. (Additional reporting by Stuart Grudgings in Washington)

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