BRUSSELS (Reuters) - Italy and Hungary, two of the Kremlin's closest allies in Europe, said on Monday there could be no automatic extension of the European Union's sanctions against Russia, the most public sign yet of fraying unity on how to deal with Moscow.

Two years after the West imposed economic sanctions over Russia's annexation of Crimea and its support for separatists in eastern Ukraine, the EU's resolve is at risk of ebbing because of the stalled Minsk peace process, diplomats say.

While EU governments last week extended asset freezes and travel bans on Russians and Russian companies, there is less consensus on whether to prolong more far-reaching sanctions on Russia's banking, defense and energy sectors from July.

"We cannot take for granted any decision at this stage," Italian Foreign Minister Paolo Gentiloni told reporters after a meeting with his EU peers in Brussels, where Russia's EU policy was discussed for the first time in more than a year.

However, EU foreign policy chief Federica Mogherini told a news conference such decisions were never taken without political debate, while EU officials said Monday's debate among ministers was measured.

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Some EU member states, such as Britain, the Baltic republics and Poland, argue that sanctions remain a necessary response to what they see as an expansionist Russia. Hungary, Italy and Greece stress its importance as a trade partner, a supplier of energy and a major player in attempts to end war in Syria.

"You cannot decide on sanctions by sweeping the issues under the carpet," Hungary's foreign minister, Peter Szijjarto, said. "We believe that the question of sanctions should be decided at the highest level. It cannot be automatic," he said.

But Lithuania's foreign minister, Linas Linkevicius, whose country was part of the Soviet Union until 1990, told Reuters that, following the debate among ministers on Monday, "there is no revision of policy".

Echoing that, Poland's Foreign Minister Witold Waszczykowski said that "the view is negative as regards the internal situation in Russia and its foreign policy".

DON'T MENTION THE 'S' WORD

Tellingly, after a long discussion, sanctions were not discussed by foreign ministers, partly because the debate was chaired by Mogherini to avoid exacerbating the divisions. Instead, EU officials - who help marshal the bloc's foreign policy - sought to gauge the mood.

One of the biggest points of contention was whether Mogherini, an Italian, should visit Russia at a time when the EU is demanding that Russia release Ukrainian pilot Nadezhda Savchenko, who is on a hunger strike, on humanitarian grounds.

Waszczykowski said he suggested to ministers that Russian Foreign Minister Sergei Lavrov first come to Brussels.

Italy, Greece, Cyprus and Hungary are among the EU states most skeptical about the sanctions, while European farmers, who once exported heavily to Russia, want to see markets reopen and protested in Brussels on Monday. Moscow has imposed its own tit-for-tat sanctions against many EU food imports.

Italian Prime Minister Matteo Renzi briefly held up a decision to extend the sanctions late last year, saying they could not be rushed through.

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However, the United States says lifting Western sanctions are conditional on Russia complying with the terms of the Minsk peace process. Moscow denies any military involvement.

"Today Russia faces a choice between the continuation of economically damaging sanctions and fully meeting its obligations under Minsk," U.S. Secretary of State John Kerry said on Sunday in Paris.

In comments that some EU diplomats took as Moscow pressing for sanctions relief, Lavrov said on Sunday he hoped the United States would be willing to compromise on the Minsk process.

(Additional reporting by Francesco Guarascio in Brussels and John Irish in Paris; Editing by Louise Ireland)