The aim of Russia's military operation in Syria is not to keep President Bashar al-Assad in power but to defeat Islamic State militants, Russian Prime Minister Dmitry Medvedev said on Saturday.

Russia began air strikes in Syria in late September, in a move which Moscow says is weakening Islamic State militants but which Western powers say aims to support Assad.

Some of Russia's air strikes have hit groups which are not affiliated to Islamic State but are trying to unseat Assad, and are backed by the United States and its allies.

"Russia, the United States, and all other states that have a stake in seeing peace in this region and in Syria, and a strong government, too, should be discussing precisely political issues," Medvedev said in an interview with Rossiya TV channel.

"It does not really matter who will be at the helm. We don't want ISIS to run Syria, do we? It should be a civilized and legitimate government. This is what we need to discuss," Medvedev said, using another name for the Islamic State.

Asked whether Syria had to be ruled by Assad, Medvedev said: "No, absolutely not. It is up to the Syrian people to decide who will be the head of Syria.... At the moment, we operate on the premise that al-Assad is the legitimate president."

The U.S. President Barack Obama said on Friday there was no meeting of the minds with Russia's President Vladimir Putin over the continuing rule of Assad, and that the Syrian civil war could only end with a political solution leading to a new inclusive government.

According to Russia, its air force has made 669 sorties, hitting 456 targets in Syria, since the start of the operation on Sept. 30.

(Reporting by Polina Devitt; Editing by Christian Lowe and Raissa Kasolowsky)