UNITED NATIONS (Reuters) - Iraq's government would welcome Russian air strikes against Islamic State and was receiving information from both Syria and Russia on the militant group, Prime Minister Haider al-Abadi said on Thursday.

The United States has led air strikes against Islamic State in Iraq for more than a year, but Baghdad has repeatedly bemoaned the lack of engagement and air support for Iraqi forces trying to regain territory against the group.

On Wednesday, Russian warplanes began air strikes in neighboring Syria, saying it would hit Islamic State "and other terrorist groups."

Abadi, asked by France 24 television whether he had discussed air strikes with Russia in his country, said: ""Not yet" and "it is a possibility. If we get the offer we will consider it and I would welcome it."

Russian Foreign Minister Sergei Lavrov said at a news conference that Moscow was not planning to expand its air strikes to Iraq.

"We were not invited or asked," Lavrov said. "We are a polite people as you know. We don't come if we're not invited."

Russian warplanes that joined the fight in Syria bombed a camp run by rebels trained by the CIA, the group's commander said, putting Moscow and Washington on opposing sides in a Middle East conflict for the first time since the Cold War.

"We were expecting the international coalition, Americans to bring massive air power to protect our forces," Abadi told France 24 on the sidelines of the annual United Nations General Assembly.

"We haven't received that. At the moment we are getting support, but it's not major, it's limited. What matters for us is how best to fight Daesh (Islamic State.)"

Iraq's military joint operations command said on Sept. 27 its military officials were cooperating on intelligence and security in Baghdad with Russia, Iran and Syria to counter the threat from Islamic State.

"It is in our interest to share information with Russia. Russia has a lot of information. The more information we gather the more I can protect the Iraqi people," Abadi said.

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Iraqi officials say the agreement to share intelligence with Russia did not mean the United States would lose influence with the Baghdad government. But diplomats and officials said Abadi may use the growing Russian presence as leverage against the Americans as he seeks more weapons from Washington.

Abadi said Baghdad had also been getting "massive" and "very useful" information on Islamic State from the Syrian government.

Abadi also said that the number of Iranian experts and advisers in his country "did not exceed 110" and "they are giving us expertise, training and know-how."

"Iran is helping us. They don't have soldiers or boots on the ground," Abadi said.

When asked whether he believed that Russia had targeted non-Islamic State targets in Syria, Abadi said Russian President Vladimir Putin had told him that it was in Moscow's interests to hit the group because he feared Russian Islamist fighters could return to Russia carry out attacks.

"I can see a sea change (in the fight against Islamic State), but I hope it is in the right direction," Abadi said. "Our aim is to bring everybody together to fight Daesh and not fight among themselves."

(Reporting by John Irish at the United Nations; Editing by David Storey and Grant McCool)