Athens' ATG equity index, which has fallen by more than 20% in 2014 on concerns about a disorderly exit by Greece from its international bailout, rose 1.9% - recovering from a 1.4% fall on Friday.
Greek Prime Minister Antonis Samaras offered on Sunday to bring pro-European independents into the government and hold new elections in late 2015 if lawmakers back him to elect a new president.
Although largely a ceremonial post, if the 300-member parliament does not choose a president by Dec. 29, elections will have to be held by early February, potentially putting bailout negotiations at risk.
Nevertheless, some traders expected Greece to avoid new elections. "Greece should be able to resolve its issues," said Securequity sales trader Jawaid Afsar.
Energy stocks also fared well.
The STOXX Europe 600 Oil & Gas Index rose 2.1 percent as Brent crude oil futures advanced by more than 2 percent toward $63 a barrel, continuing a recovery from a slump in the price over the last month.
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