The U.S.-backed Free Syrian Army said Monday that it will not accept Russia's offer to help them fight against the Islamic State group until Moscow stops bombing rebel bases.

Russian Foreign Minister Sergei Lavrov said Saturday that the Russian air force would be willing to provide air support to "patriotic" rebels fighting against the Islamic State group. "We are ready to support from the air the patriotic opposition, including the so-called Free Syrian Army,'' he said in an interview on Russian state television, according to the BBC.

Moscow has been conducting bombings since entering the Syrian conflict on Sept. 30, reportedly striking both the Islamic State group and the Western-backed rebels fighting to overthrow Syrian President Bashar al-Assad. Russia insists it is only targeting "terrorists," according to Reuters.

"They should stop attacking our bases and then we can talk about future cooperation," a Free Syria Army spokesman told BBC.

Issam al-Rayyes, spokesman for the Southern Front of the Free Syrian Army, said it would not immediately reject the offer for air support, but told Reuters, "Their words are not like their actions. How can we talk to them while they are hitting us?"

Al-Rayyes told the BBC: "So we didn't turn down the offer. We just said we don't need their help now. If the Russians are serious in their offer they should stop immediately targeting our bases and targeting the civilian areas." 

"You know the Russians - always their words are different from their actions," he added.

Meanwhile, the United States and Saudi Arabia agreed over the weekend to respond to Russian air strikes in support of Assad by intensifying their own military and diplomatic support for the rebels.

U.S. Secretary of State John Kerry met King Salman of Saudi Arabia in Riyadh and "pledged to continue and intensify support to the moderate Syrian opposition while the political track is being pursued," the State Department said in a statement, according to Reuters.