CBS reported the statement came as voters in Crimea decided whether to secede from Ukraine and as European and American officials discuss sanctions to impose on Moscow as early as Monday.
The former Soviet satellite has been in turmoil since November when then President Viktor Yanukovych decided against closer relations with the European Union to protect Kiev's ties to Moscow. Yanukovych was ousted last month and fled to Russia.
Sunday's announcement came after Russian troops seized control of a gas plant just inside Ukraine's border, allegedly to protect the facility from "terrorist attacks."
At least 80 soldiers were deployed to Strelkovoye, just outside the Crimea's regional border, to take over the natural gas terminal Saturday, The New York Times reported.
A Russian official, speaking anonymously, told the Pravda-Ukraine the seizure of the gas plant was to protect the station from "terrorist attacks," the BBC reported.
Ukraine also sent troops to the terminal Saturday, the Times said. There were no reports of shots being fired.
The Ukrainian Foreign Ministry said Ukraine "reserves the right to use all necessary measures" to stop what it called "the military invasion by Russia."
Sanctions against Russia being discussed by Europe and the United States include banning certain Russian military leaders, business tycoons and parliamentarians from traveling to the United States or Europe and freezing any assets they had in either place.
American officials said they do not plan on sanctioning Russian President Vladimir Putin because he is the head of state, nor will they sanction Lavrov, who will need to be able to travel for any future diplomatic talks.
Meanwhile, the United Nations Security Council's resolution on Crimea was vetoed by Russia Saturday.
The council was voting to reaffirm Ukraine's "sovereignty, independence, unity and territorial integrity" and declare Crimea's referendum invalid.
Thirteen members of the council voted in favor of the resolution while Russia vetoed it and China abstained.
Before the vote, the Russian Permanent Representative to the United Nations, Vitaly Churkin, said it was "no secret" Russia planned to vote against the resolution