In an interview with state-controlled RT television on April 23, Lavrov said: "If we are attacked, we would certainly respond."
His comments came after Ukraine's acting President Oleksandr Turchynov ordered the resumption of an "antiterrorist" operation against pro-Russian rebels in eastern Ukraine.
Turchynov cited the discovery of two apparently tortured bodies near the rebel-held town of Slovyansk. One of those killed has been identified as a local politician from Ukraine's ruling party.
Lavrov linked the announcement of the resumption of the Ukrainian security operation to the April 22 visit to Kyiv by U.S. Vice President Joe Biden, who renewed Washington's support for the Ukrainian goverment.
Lavrov said Moscow believes the United States is "running the show" in Ukraine.
Lavrov compared the situation in Ukraine to the brief 2008 war between Russia and Georgia, when Russian forces invaded Georgia in support of pro-Russian South Ossetian separatists.
Lavrov said Ukraine is "just one manifestation of the American unwillingness to yield in the geopolitical fight."
Ukraine's Security Service said the militant separatists who control Slovyansk were to blame for the killing of politican Volodymyr Rybak. The service alleged that a Russian lieutenant colonel was involved the death.
In his remarks on April 22, Turchynov said such crimes were being carried out "with the full support and indulgence" of Russia.
Ukraine's Deputy Prime Minister Vikaliy Yarema told reporters on April 23 that Turchynov's order to restart the security operation was being carried out.
However, he said no military actions were taken overnight.
Rebels in Slovyansk are also suspected of having detained American journalist Simon Ostrovsky, who works for the U.S. website Vice News.
The State Department said on April 23 that it was "deeply concerned" by reports that Ostrovsky had been kidnapped.