Speaking to reporters in Tel Aviv ahead of meetings with his Israeli counterpart and the president, Lavrov said: "We condemn what radicals have done in Gaza. Everybody, including Hamas's militant wing, should understand that Palestinian unity cannot be achieved in an uncivilized way."
At least 115 people have been killed and hundreds injured in armed clashes between Hamas and the pro-presidential Fatah movement in Gaza since early June.
Hamas has ousted Fatah forces and now controls Gaza. Fatah, led by President Mahmoud Abbas, who has dissolved the coalition Cabinet with the Islamists and established an emergency government, is in control of the West Bank. Abbas asked Israel Monday to allow Palestinian troops now based in Jordan into the West Bank.
The new Fatah government, led by Prime Minister Salam Fayyad, has received the backing of most Western nations and of the more moderate Arab states.
Earlier Tuesday, the envoys of the "Quartet" mediating in the Israeli-Palestinian conflict - Russia, the United States, the European Union, and the United Nations - met in Jerusalem in a bid to revive peace efforts in the region.
"The international community should focus its efforts on a peaceful solution to the problem," said Lavrov, who will meet with Prime Minister Ehud Olmert in Jerusalem Wednesday and Palestinian President Mahmoud Abbas in the West Bank's Ramallah.
The minister also said he would try to help in the evacuation of the remaining Russian nationals from Palestinian lands.
Seventy-three Russians left the Palestinian territory June 21. But dozens more, mainly Russian women married to Palestinians, remain in the violence-torn region. Russian diplomats are considering another round of evacuation for Russians left in the region.
"We hope this problem will be resolved. It will be discussed at talks with my Israeli counterpart [Tuesday] and the prime minister tomorrow," he said.