Russia's aid was shipped in an Ilyushin-76 cargo plane and included 40 tonnes of canned food, baby food, rice and sugar.
Samardzic said three more shipments including more food and medical aid were expected by April 10.
"This is important help for the survival of Serbs in Kosovo," he said.
No details have been given about how the aid will be distributed among the 100,000 or so Serbs living in Kosovo.
Vladimir Putin, Russia's president, ordered the aid at Serbia's request.
He said the aid should be distributed regardless of ethnicity and "without political colouring".
However, Kosovo's ethnic Albanian leaders have said that Moscow should coordinate shipments with Pristina, Kosovo's capital, rather than Belgrade.
Kosovo's February 17 declaration of independence was quickly recognised by the United States and its key European allies.
But Serbia and Russia have rejected Kosovo's statehood as illegal under international law.
Belgrade has sought in past weeks to retain control over Serb-held areas in Kosovo, a move that could lead to a de facto division of the territory.
Clashes last month between Serbs, UN police and Nato peacekeepers in Kosovo left a Ukrainian policeman dead and dozens of people on both sides injured.
Serbs also say a new European Union administrative mission is illegal.
Lavrov said Russia was working to prolong the UN mission established in Kosovo in 1999, after a Nato air war ended a Serb crackdown against Kosovo separatists.
Speaking to the Duma, Russia's parliament, he said: "We are taking concrete measures to prevent the use of force to compel the Kosovo Serbs to accept Kosovo's independence.
"Making Serbs submit to recognizing the legitimacy of the European Union mission is illegitimate. I am concerned that the developing situation in Kosovo is not over."