By Ahmed Rasheed and Ned Parker

BAGHDAD (Reuters) - Iraq has told President Barack Obama's envoy that the U.S.-led coalition battling Islamic State needs to do more to help Iraq defeat the jihadists controlling large areas of the north and west of the country.

Parliament speaker Selim al-Jabouri said he delivered the message in a closed meeting with retired U.S. Marine General John Allen, who visited Baghdad this week for talks with Prime Minister Haidar al-Abadi's government.

"Until now our feeling is that the international support is not convincing," Jabouri told Reuters in an interview on Wednesday. "We might see participation here or there, but it is not enough for the tough situation we are passing through."

Islamic State fighters swept through north Iraq last June, seizing the city of Mosul in a lightning offensive and approaching the capital Baghdad as Iraq's army disintegrated.

The Sunni Islamist advance was contained by Shi'ite militia allied to the Baghdad government and Kurdish peshmerga fighters, backed by U.S.-led air strikes. U.S. soldiers who withdrew from Iraq in 2011, eight years after invading to overthrow Saddam Hussein, have also returned to help re-train Iraqi forces.

But Jabouri, one of Iraq's most senior Sunni politicians, said he told Allen that the international community must "activate its role" because Iraq feels that, despite air strikes and other assistance, it is fighting largely on its own.

Jabouri's frustration echoed the more guarded comments issued by Shi'ite prime minister Abadi after his own meeting with Allen on Tuesday.

A statement from Abadi's office after the talks said US-led alliance should "increase the tempo of the effective air strikes on Islamic State positions", and also called for the training program for Iraqi security forces to be expanded.

Abadi's official Twitter account said the two men had agreed on both those points.

For his part, Allen painted an optimistic picture on Wednesday of the ongoing war against Islamic State.

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"Our global coalition to counter (Islamic State) grows stronger as does our collective commitment to the people of Iraq and the country of Iraq," he told reporters in Baghdad, describing his travels to build an international alliance against Islamic State.

The war in Iraq started one year ago amid clashes between then Prime Minister Nuri al-Maliki's Shi'ite-dominated security forces with Sunni protesters and tribesmen in western Anbar province.

Islamic State, which already controlled swathes of eastern Syria, took advantage of the violence to move into Anbar's two main cities of Falluja and Ramadi.

In June, Islamic State seized the north's largest city of Mosul and towns across northern Iraq fell to the militants. The jihadists also expanded their control of large swathes of Anbar.

After Islamic State nearly overran Iraq's Kurdish region in the first week of August, President Obama ordered air strikes on Islamic State and assembled a coalition of western and Arab countries against Islamic State. The US government has described Iraq as the central battleground in the war.

A former US official recently described the White House's approach to Iraq as " passive tough love" - not allowing the United States to get to drawn into Iraq, but still helping the country defeat Islamic State.

(Reporting By Ned Parker and Ahmed Rasheed; Editing by Dominic Evans)