LONDON, Feb 17 (Reuters) - European shares fell on Tuesday after talks between Greece and euro zone finance ministers over the country's rescue package broke down, raising doubts about Athens' future in the euro.

The pan-European FTSEurofirst 300 index was down 0.3 percent at 1,497.06 points at 0803 GMT. Greece's Athex share index was due to open at 0830 GMT.

Euro zone banks, which have a large exposure to the region's sovereign debt market, led the declines, falling 1 percent.

After the market close on Monday, Greece rejected a proposal to request a six-month extension of its international bailout package as "unacceptable". Dutch Finance Minister Jeroen Dijsselbloem, who chaired the meeting, said Athens had until Friday to request an extension, otherwise the bailout would expire at the end of the month.

"It's a big risk and the pressure is immense," said Joost Van Leenders, chief economist of multi asset solutions at BNP Paribas Investment Partners. "The parties have to move and the room for manoeuvre is pretty small."