He rejected a call by the American envoy to the UN Security Council to sever ties with the North after its latest ballistic missile test.
Russia argues sanctions do not work and advocates negotiations instead.
The US has warned that North Korea’s government will be “utterly destroyed” if war breaks out.
On Wednesday, the North tested its first missile in two months, saying the continental US was now within striking distance.
However, defence experts have cast doubt on its ability to master the technology needed to launch a missile carrying a warhead capable of re-entering the Earth’s atmosphere.
Speaking on a visit to the Belarussian capital Minsk, Mr Lavrov asked whether America was actively seeking to destroy North Korea.
“One gets the impression that everything has been done on purpose to make Kim Jong-un snap and carry out further inadvisable actions,” he said.
The Americans, he said, “should explain to us all what they’re after”.
“If they want to find a pretext for destroying North Korea, as the US envoy said at the UN Security Council, then let them say it outright and let the supreme American leadership confirm it.”
Calling for new talks with North Korea, Mr Lavrov added: “We have already emphasised several times that the squeeze of sanctions has essentially come to an end, and that those resolutions which introduced the sanctions should have included a requirement to renew the political process, a requirement to renew talks.
“But the Americans completely ignore this requirement and I consider this a big mistake.”
After China, Russia is one of the few states with which North Korea still has good relations. Both Russia and China wield a veto at the UN Security Council. (Courtesy BBC)