Speaking at a Moscow diplomatic academy, Tzipi Livni said the international community's failure to back Israel in its fight against Gaza-based insurgents could eventually result in the enclave - currently controlled by the hard-line Islamic group Hamas - transforming into a fully-fledged state ruled by extremists.
Livni's visit to Russia takes place against the backdrop of a vicious circle of rocket attacks on Israel from Gaza and Israeli retaliatory strikes on the enclave of some 1.5 million people.
Palestinian radicals stepped up attacks after an Israeli raid in Gaza killed 19 people on Tuesday. On Wednesday, five Palestinians, including three civilians and a teenage boy, were killed in an Israeli air strike on the territory.
The Israeli military said insurgents had launched at least six rockets at Israel on Thursday, one of them slightly injuring an Israeli woman.
Livni said the fight against extremism should be accompanied by support for moderate Palestinian groups, as well support for the Palestinian judiciary and the tackling of social problems, two measures she said were vital for progress in the peace process.
Ongoing violence has complicated peace talks between the Jewish state and the moderate Palestinian groups led by President Mahmoud Abbas. The parties pledged at a U.S.-hosted summit in November to resume talks after a seven-year hiatus and reach a deal in 2008 on forming a Palestinian state.
Other stumbling blocks in the negotiations include Tel Aviv's announced plans to build more homes near Jerusalem, state borders, the fate of Jerusalem and Palestinian refugees.
Opening talks with her Russian counterpart, Sergei Lavrov, Livni said Israel hoped for support from Russia in talks with the Palestinians, a co-sponsor in the Middle East peace process.
Livni's visit comes a day after U.S. President George W. Bush rounded off his eight-day tour of the Middle East with a brief visit to Egypt to discuss, among other issues, the Egyptian-Gaza border, which Israel says is a source for arms deliveries to Hamas.
