By Thorsten Severin
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Addressing a packed parliament before the vote, Merkel urged the lower house Bundestag to fulfill its "historic duty" and said Europe was in its toughest phase since the end of World War Two.
"No one should take for it for granted that there will be peace and affluence in Europe in the next half century," said Merkel, a pastor's daughter brought up in Communist eastern Germany.
"The world is watching Germany and Europe to see if we are ready and able to take responsibility. If the euro fails, Europe fails," said Merkel, in a characteristically sober tone.
The vote binds Merkel to sticking closely to the text of the motion passed by the Bundestag, boosting her bargaining power at the Brussels summit on issues such as the European Central Bank's involvement in tackling the crisis.
The prospects of a comprehensive deal looked dim, however, with disagreements remaining in several crucial areas.
The Bundestag's vice president said of the 596 lawmakers who voted, 503 backed the motion, 89 opposed it and there were four abstentions.
"With its clear, cross-party majority, the German parliament has strengthened the hand of the German government in its negotiations on fighting the euro debt crisis," said Foreign Minister Guido Westerwelle after the vote.
"With this, the government can fight forcefully for our interests," added Westerwelle, a member of the Free Democrats (FDP), Merkel's junior coalition partner.
In a minor boost to her waning authority at home, she won the vote without having to rely on opposition support.
However, 15 rebels from her own center-right coalition either voted against the motion or abstained, highlighting the struggle Merkel faces in convincing Germans of the need for Europe's biggest economy to help its indebted partners.
Merkel is battling sliding ratings for herself and her coalition over her handling of the euro zone crisis. Critics at home and abroad have accused her of dithering, thereby exacerbating the debt crisis, and frustration is rife.
The proposals to increase the effectiveness of the 440 billion euro ($610 billion) European Financial Stability Facility (EFSF) without pouring more taxpayers' money into it, have been the subject of fierce debate in Germany, the biggest contributor to the rescue fund, and the rest of the euro zone.
Disagreements remain, including over how to scale up the EFSF.
One option is to use it to offer guarantees to purchasers of new euro zone debt, the other to use part of its capacity to set up a special purpose investment vehicle to attract money from sovereign wealth funds and other investors. A combination may also be possible.
Merkel said it was justifiable to take the chance of higher risks stemming from leveraging the EFSF and that failure to give the fund more firepower would be irresponsible.
"The goal of the meeting tonight must be to get a result under which Greece will by 2020 have a debt to gross domestic product ratio of 120 percent," said Merkel.
Under the sustainability scenarios put forward by Greece's 'troika' of lenders -- the European Commission, European Central Bank and International Monetary Fund -- that would mean a 50 percent writedown for private sector bondholders.
The role of the European Central Bank in resolving the crisis is also subject to dispute, France wanting a deeper and more direct ECB involvement, something Germany strongly opposes.
The motion passed by German lawmakers states that the EFSF cannot be financed through the ECB and with a leveraged EFSF, the central bank will no longer need to buy bonds on the secondary market.
German lawmakers said this was not necessarily a rebuff to them as the phrase in their motion expresses an expectation and stops short of saying the ECB cannot buy bonds if necessary.
Merkel's hands have been tied by a Constitutional Court ruling last month, which demanded a greater say for German lawmakers. That has frustrated some EU leaders eager to implement quick solutions.
Lawmakers -- either in the lower house's full session or its 41-member budget committee -- will have to be consulted again about the EU leaders' summit conclusions.
(Additional reporting by Sarah Marsh, Alexandra Hudson, Madeline Chambers and Annika Breidthardt; Writing by Madeline Chambers; Editing by Ruth Pitchford, John Stonestreet)