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Merkel was addressing parliament, which is expected to vote by a clear margin for the euro zone to start talks on the new aid programme even though Finance Minister Wolfgang Schaeuble has questioned whether it will succeed.
Schaeuble himself has suggested that Greece might be better off taking a "time-out" from the euro zone to sort out its daunting economic problems.
Read more from our special coverage on "GREECE CRISIS"
But Merkel argued for negotiating a new deal with Greece to prevent the country's exit from the euro - the "Grexit" that might undermine the entire currency union.
"The alternative to this agreement would not be a 'time-out' from the euro ... but rather predictable chaos," she told the Bundestag lower house. "We would be grossly negligent, and act irresponsibly, if we didn't at least attempt this way."
Popular misgivings run deep in Germany, the euro zone country which has contributed most to Greece's two bailouts since 2010, about funnelling yet more aid to Athens.
But the conservative chancellor expressed scepticism that a temporary Greek departure from the common currency would solve the problem, saying neither Greece nor the other 18 euro zone member countries were willing to accept the idea. "Therefore this way was not viable," she added.
Nevertheless Merkel thanked Schaeuble - her most powerful ally - for his work in the long, gruelling talks which produced the new bailout plan last weekend. Lawmakers gave him resounding applause while Schaeuble nodded and gave a wry smile.
Despite his misgivings, Schaeuble lined up with his boss. "I ask you all to vote for this request today. The government didn't submit the request easily," he told the Bundestag. "It's a last attempt to fulfil this extraordinarily difficult task."
Merkel also won support from the Social Democrats, the junior coalition partner. "Every debate about a Grexit must now belong to the past," said Social Democrat leader Sigmar Gabriel, who is also vice chancellor.
Lawmakers from Merkel's conservatives and the Social Democrats already voted overwhelmingly in favour of the euro zone opening talks with Athens in test ballots held on Thursday. [ID:nL5N0ZW4XZ] This indicates Merkel is likely to get the mandate she needs from the Bundestag, with some opposition parties also expected to vote 'Yes' at the end of the debate.
Seven Reasons
That view is far from unanimous across the nation.
"Seven reasons why the Bundestag should vote 'No' today," ran a headline in the mass-selling Bild daily, listing 'Grexit is the better solution' and 'our grandchildren will pay' among its reasons.
The Greek parliament approved the new bailout offer in the early hours of Thursday, although Prime Minister Alexis Tsipras had to rely on opposition support after some lawmakers from his left-wing Syriza party rebelled.
Tsipras moved on Friday to replace his energy minister, one of the rebels, a government source said.
Some Syriza members refuse to accept the demands for yet more austerity and reform included in the deal with Greece's creditors. The Greek electorate has already rejected an earlier offer in a referendum, and the latest is even tougher.
Still, the Greek parliamentary approval opened the way for European action to stave off Grexit, at least for the time being. The European Central Bank increased emergency funding to keep the country's banks from collapse on Thursday.
European Union finance ministers also approved 7 billion euros in bridge loans to Greece, allowing it to avoid defaulting on a bond payment to the ECB next Monday and clear its arrears with the IMF.
With Merkel under domestic pressure from lawmakers who have lost trust in Greece, the creditors agreed the tough deal at the weekend demanding that Athens cut pensions, raise value-added tax, and set aside 50 billion euros ($54 billion) of state assets to sell off.
Conservative lawmaker Mark Helfrich told Deutschlandfunk radio he would still vote 'No', adding: "This is about ruined trust." In a sign of frustration with Athens, 48 conservatives in Thursday's test vote opposed new negotiations, according to participants.
Some members of the opposition Greens plan to abstain, saying they want Greece to stay in the euro but reject austerity as a cure for its ills. "Another bloodletting won't make Greece more healthy ?again," said lawmaker Katrin Goering-Eckhardt, backing IMF calls for Greece's debt burden to be eased.
That fell on deaf ears with Merkel and Schaeuble, who said European law did not permit a "haircut" writing off part of the debt.
German conservatives have accused Tsipras of blackmail for saying other weaker euro zone countries would slide into crisis if Greece were forced out of the euro. But Gregor Gysi of the Left party, Syriza's ideological counterpart in Germany, turned the tables.
"You're not being blackmailed - you're the blackmailers yourselves" said Gysi. "Mr Schaeuble, I'm sorry but you're in the process of destroying the European idea."
($1 = 0.9186 euros)
