Merkel said the money would not only help Greece, which has been battered by the bond markets, but would help the "stabilization of the euro as a whole and, therefore, help the people of Germany."
The remark was a nod to the popular discontent in Europe's biggest economy about having to pay so much to help a fellow European Union country that many Germans feel has been fast and loose with its finances for years.
The European Central Bank, meanwhile, suspended its rating limits on Greek debt.
Both moves were mandatory after European governments and the International Monetary Fund agreed Sunday to give euro110 billion ($145 billion) in loans to Greece over three years. The loans came after Athens adopted a new round of austerity measures that provoked fresh uproar among Greek workers.
IMF officials say Greece could start receiving money from the rescue package in about a week.
Germany will contribute euro8.4 billion ($11.1 billion) for the first year of the bailout this year, followed by euro14 billion ($18.5 billion) over 2011 and 2012. The money will come in the form of credit extended to Greece the KfW Development Bank, which is backed by the German government.
The draft law backed by the cabinet now needs to pass both houses of parliament. Merkel has fast-tracked it, hoping to have it approved this week. The main opposition parties have already said they won't block the bill.
"This is the only way for us to return the euro to stability," Merkel said of the Greek bailout. "It is a sustainable program, spread out over many years."
Merkel's government had insisted on the latest Greek austerity package before it would move to free up aid. Her party faces a crucial regional election Sunday in North Rhine-Westphalia, Germany's most populous state, and many German voters are angry that their taxes are being used to bail out Greece while Germany itself struggled through years of budget-tightening to stimulate its own economy.
"This is just the tip of the iceberg and I am afraid of it," Werner Selmer told AP Television News at Berlin's main train station. "Is this necessary? Should we do this? I think yes, my feeling is yes, but I have a bad feeling, a very bad feeling."
In Rome, Italian Foreign Minister Franco Frattini criticized Berlin for dragging its feet.
"The later you intervene, the worse it gets." Frattini said Monday, noting that the initial figure mentioned was "euro50 billion - 10 days later we decided on euro110 billion."
Greece announced more austerity measures on Sunday worth euro30 billion ($40 billion) through 2012 - including public service and pension pay cuts and higher taxes. In response, about 1,000 garbage collectors and other striking municipal workers marched to the Greek parliament on Monday, chanting "trash for parliament, not the landfill!"
But Prime Minister George Papandreou insisted the new measures are vital for Greece's financial survival.
"This is a chance for a fresh start," Papandreou said Monday. "We are making changes that should have happened years ago."
The ECB, the central bank for the 16 nations that use the euro, said Monday it was suspending the minimum credit rating requirement for all existing and new debt instruments "issued or guaranteed by the Greek government."
The decision by the Frankfurt-based bank ensures that Greek debt can be used as collateral in ECB lending operations, despite the fact that Standard & Poor's cut Greece's rating to junk status last week.
"Clearly, desperate times call for desperate actions, and today's ECB decision is one step in the right direction," analysts with the Royal Bank of Scotland wrote in a research note.
Greece's new austerity measures are expected to exacerbate its recession, but the massive rescue plan will include euro10 billion ($13.3 billion) for a "stabilization fund" to support Greek banks, Greece's Deputy Finance Minister Philippos Sachinidis told state television on Monday.
In Paris, French Finance Minister Christine Lagarde defended the bailout, telling Europe-1 radio it is "not a donation, it is not a subsidy" but a loan to push Greece to clean up its public finances. She was presenting a budget amendment later Monday to the lower house of parliament allowing the government to release French aid funds for Greece.
Lagarde also said she will authorize France's market regulator to closely monitor ratings agencies, which EU officials have blamed for fueling the Greek debt crisis.
Greek labor unions, upset over a new round of spending cuts, have planned another general strike for Wednesday.
"These cuts will kill our income. Pensions in Greece are already very low," said Dimos Koumbouris, head of a pensioners' association, told the AP.
He feared the austerity measures, which cut back on holiday bonuses paid to public servants and pensioners, will force them to curtail their spending.
"Many retired people wait for their holiday bonuses to buy clothes and even extra food," he said. "How will these people get by now?"
The Athens Stock Exchange opened up on the news of the loan agreement, before dropping back 1.24 percent to 1,846. Spreads on Greek bonds were down to 574 from above 600 in the morning.
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Gatopoulous reported from Athens. Associated Press news editor Angela Charlton in Paris and Associated Press writers David Rising and Matt Moore in Berlin contributed to this report.
