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The vote was seen as a test of Chancellor Angela Merkel's authority, as some in her coalition vowed to oppose the bill. Many Germans are against committing more money to prop up struggling eurozone members, such as Greece.
523 MPs approved the bill, 85 voted against and three abstained in Germany's 620-seat Bundestag. Nine members were not present.
The measure is expected to pass in Germany's upper house of parliament, where it will be put to a vote on Friday.
All 17 countries that use the euro must ratify the commitment to boost the bailout guarantees to €440 billion (£383 billion).
So far, 10 have approved the measure.