"We have informed the UN in New York and Geneva that there is no longer a problem with the delivery of humanitarian cargo to eastern Aleppo," he told reporters in Rome, according to a RIA Novosti news agency transcript.
Russia has previously decreed the establishment of humanitarian corridors, but the UN has never used them for lack of security guarantees.
Speaking alongside his Italian counterpart Paolo Gentiloni, Lavrov said approval from the Syrian government of President Bashar al-Assad remained essential.
"It is necessary to agree with the Syrian government on the passage of these convoys, which are no longer threatened," RIA Novosti quoted the top diplomat as saying.
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"The UN is still thinking about how it could be done," he added.
Russia, Assad's main ally, yesterday proposed setting up four humanitarian corridors into east Aleppo to bring in aid and evacuated severely wounded people.
Moscow, however, was criticised at Wednesday's UN Security Council meeting on Syria, with British ambassador Matthew Rycroft accusing Russia of supporting "a deliberate act of starvation and a deliberate withholding of medical care."
More than 300 civilians, including dozens of children, have been killed in east Aleppo since the government offensive began, according to the Observatory.