Despite the German rejection, Greece's wording of a document seen by Reuters appeared to go substantially toward the position taken by euro zone finance ministers in early negotiations. That reassured investors a deal was not far away.
In Asia, Japanese stocks hit 15-year highs.
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Ten-year bond yields in Spain, Italy and Portugal - the countries most vulnerable to the Greek crisis - fell five-seven basis points to 1.54 per cent, 1.56 per cent and 2.27 per cent, respectively. They were little changed after a German finance ministry spokesperson said the proposal did not correspond to criteria agreed by the Eurogroup on Monday.
The broader FTSEurofirst 300 index was up a touch at 1516.30 after reaching a seven-year high of 1.517.98 points when the Greek proposal was reported and a low of 1,504.03 before that. US stock market futures SPc1 were steady.
"We should now get a definitive agreement soon," Rabobank rate strategist Lyn Graham Taylor said.
Greece's main stock market index rose 1.1 per cent and banking stocks rose 5.8 per cent. Greek 10-year bond yields fell 38 basis points to 10.05 per cent.
The Greek request for a six-month extension to its euro zone loan agreement came as it was weeks away from running out of cash. Crucially, Greece agreed the extension would be monitored by the EU Commission, European Central Bank and International Monetary Fund - a retreat by Prime Minister Alexis Tsipras, who had vowed to end cooperation with "troika" inspectors.
The euro held steady, after gaining against the dollar on Wednesday after minutes from the Federal Reserve meeting in January showed Fed officials were concerned about hiking interest rates too soon. The dollar fell after the minutes but was broadly stable on Thursday.