MOSCOW/WASHINGTON, Sept 30 (Reuters) - Russia launched air strikes in Syria on Wednesday in the Kremlin's biggest Middle East intervention in decades, but Moscow's assertion that it had hit Islamic State was immediately disputed by the United States and rebels on the ground.

The air strikes plunged the four-year-old civil war in Syria into a volatile new phase as President Vladimir Putin moved forcefully to assert Russian influence in the unstable region.

Moscow and Washington offered conflicting accounts of which targets had been struck, underlining growing tensions between the two former Cold War foes over Russia's decision to intervene. Washington is concerned that Moscow is more interested in propping up Syrian President Bashar al-Assad than in beating Islamic State.

The Russian defense ministry said the strikes targeted military equipment, communication facilities, arms depots, ammunition and fuel belonging to Islamic State.

U.S. officials said targets in the Homs area appeared to have been struck, but not areas held by Islamic State.

Russia warned the United States ahead of the strikes to keep its aircraft out of Syrian airspace, but the United States pressed forward with its campaign of air strikes against Islamic State forces and said it had targeted Islamic State near the Syrian city of Aleppo.

A U.S. official said Moscow gave Washington just an hour's notice of its strikes, which the Kremlin said were designed to help Assad, its closest regional ally, push back Islamist militants.

Notice of the attack came from a Russian official in Baghdad who asked the U.S. air force to avoid Syrian airspace during the mission, U.S. State Department spokesman John Kirby said.

In Moscow, Putin said Russian air strikes in Syria would be limited in scope and that he hoped Assad was ready for political reform and a compromise for the sake of his country and people.

"I know that President Assad understands that and is ready for such a process. We hope that he will be active and flexible and ready to compromise in the name of his country and his people," he told reporters.

U.S. Secretary of State John Kerry said Washington would have "grave concerns" if Russia hit Syrian targets where Islamic State fighters were not present. Speaking at the U.N. Security Council, Kerry also said the militant group, which is also known as ISIL and ISIS, "cannot be defeated as long as Bashar al-Assad remains president of Syria."

Striking Homs and opposition groups but not IS showed the Kremlin's primary aim was to prop up Assad, a French diplomatic source said.

Areas of the province of Homs struck by the Russians are controlled by an array of rebel groups including several operating under the banner of the "Free Syrian Army," activists, locals and rebels said. None of the sources named Islamic State as one of the groups operating in the areas hit on Wednesday. Assad views all the forces opposing him in the civil war as terrorist groups.

The Homs area is crucial to Assad's control of western Syria. Insurgent control of that area would bisect the Assad-held west, separating Damascus from the coastal cities of Latakia and Tartous, where Russia operates a naval facility.

Iyad Shamse, leader of an FSA Syrian rebel group, the Asala and Tanmieh Front, told Reuters: "There is no Islamic State in this area. The Russians are applying great pressure on the revolution. This will strengthen terrorism, everyone will head towards extremism. Any support for Assad in this way is strengthening terrorism."

He put the death toll from the Russian air strikes at 50 civilians, including children.

According to a pro-Syrian government military source, there were "five strikes against five areas in Syria's Homs." He said other areas may have been bombed too.