Lavrov said Russia was making efforts to reach an agreement with Ukraine, the International Committee of the Red Cross (ICRC), and the UN on humanitarian aid deliveries to Lugansk and Donetsk regions.
"We think this is a pressing issue that admits of no delay. This issue is under control of the Russian president," Lavrov said.
"We hope we will be able to agree relief aid deliveries to those who need them as soon as possible," he added.
"Now, our top priority is to agree on urgent humanitarian aid to the Lugansk and Donetsk regions with the Ukrainian side, with the International Committee of the Red Cross and with international humanitarian organisations within the United Nations system," he told journalists.
Lavrov: We hope we will be able to agree relief aid deliveries
The Red Cross reported on Friday that armed clashes between pro-Kiev troops and self-defence militias in the Donetsk and Lugansk regions had deteriorated the humanitarian situation in east Ukraine as thousands of families had been forced to flee their homes.
"The living conditions of the residents were worsening," the Red Cross said in a statement.
Almost 850,000 people have been forced to flee their homes since the start of Kiev's military operation in the country's southeast, of whom 730,000 have found shelter in Russia, according to data released by the office of the UN high commissioner for refugees.