The Russian Foreign Minister said David Miliband "demonstrated more understanding in searching for a way out of the deadlock in bilateral relations which are affecting certain issues following Britain's unilateral actions."
"We explained that lifting these measures could help normalize relations," Lavrov said.
The latest dispute between the countries flared up when Russia ordered the closure of British Council offices in Yekaterinburg and St. Petersburg.
The move was seen as a follow up to tensions following the murder of former Russian security officer Alexander Litvinenko in London. Moscow has refused to extradite Andrei Lugovoi, London's chief suspect in the case.
Russia also has a series of outstanding extradition requests for Britain.