By Andrea Thomas 

BERLIN--Germany's parliament on Thursday backed plans to extend Greece's bailout program by two months after Finance Minister Wolfgang Schäuble said it would help stabilize financial markets.

The plan, which has been drawn up by eurozone governments, would give Athens extra time for talks with international creditors beyond the first round of presidential elections that were held on Wednesday.

Greece has received two successive international bailouts since 2010 worth a total of EUR240 billion, with the second one due to expire on Dec. 31. The lawmakers gave Mr. Schäuble a mandate to back negotiations over a precautionary credit line worth around EUR10 billion for Greece once the current bailout program runs out.

The surprise decision by Athens to bring forward presidential elections to December from February has led to a slump in Greek stock prices, with investors worrying that the move might cause political instability and plunge the country back into turmoil.

"There is still uncertainty in financial markets, which to some degree gets triggered by the domestic situation in Greece. and increased over the past weeks," Mr. Schäuble told lawmakers. "Therefore, it would be a stabilizing signal for all, for Greece, for markets, for the eurozone as a whole if Greece meets its commitments... and then a precautionary credit line were to get decided under certain conditions."

He said backing from Germany would send "the right signal to provide as many stabilizing signals as possible in this critical phase."

The first round of presidential elections in Greece failed to provide a winner with another vote due next week, fueling concern that the Greek government might also collapse.

Mr. Schäuble said Greece is in better shape than many thought possible a few years ago. Structural reform efforts have paid off but more needs to be done, he added.

His comments come after Chancellor Angela Merkel told lawmakers that the eurozone had improved from the height of the financial crisis, but weak spots remain.

"We have this crisis under control, but we haven't yet overcome it once for all," she warned. "We haven't reached our goal yet, because the economic recovery remains fragile, mostly unemployment and foremost that of young people, is in parts of Europe still far too high and [because] the makeup of the economic and monetary union has still weak spots."

International creditors are currently in talks with Greece over further cutbacks to address Greece's public finances, but talks are in a deadlock as the two sides disagree on the need for new budget cuts and legislative measures.

Write to Andrea Thomas at andrea.thomas@wsj.com