FSA is an armed Syrian opposition faction considered moderate by Western countries, which seek the removal of Syrian President Bashar Assad from power.
"Russia should work with Security Council members to help find a diplomatic solution to the Syria crisis; to alleviate the human suffering; and to defeat IS [Islamic State]," the FCO press service said.
Russian Foreign Minister Sergei Lavrov also said Moscow was willing to reach out to FSA to discuss collaboration in the fight against ISIL militants in Syria.
UK Defense Secretary Michael Fallon urged Russia on Friday to use its influence with Syria to "find a diplomatic solution and help alleviate the humanitarian crisis" in the country.
Russia began precision airstrikes against ISIL targets last week at Assad’s request. Earlier in October, Syrian Ambassador to Russia Riad Haddad confirmed that the strikes were being carried out against armed terrorist organizations and not political opposition factions or civilians. He added that Russia’s airstrikes had destroyed 40 percent of Islamic State's infrastructure in Syria.