Merkel, whose conservatives were weakened after they won an election in September with a reduced number of seats, said she would inform the German president that she could not form a coalition, after the pro-business Free Democrats withdrew from negotiations.
The development thrust Germany into a political crisis that raised worries among investors of a new election if Merkel cannot form a minority government.
But after selling off sharply in early deals in Asia, trading down as much as 0.8 percent to hit 131.16 yen , the euro's weakest since Sept. 15, the single currency rebounded as much as 1 percent to trade flat on the day, at 132.18 yen.
"What usually happens after any news at the weekend is that Asian trading tends to be a bit less liquid, and that can exaggerate the scale of the moves; when Europe came in, markets took a more level-headed approach," said MUFG currency strategist Lee Hardman, in London.
"There's a bit of uncertainty - we don't know what the next step is going to be, whether it's going to be a minority government or fresh elections - but in terms of the bigger picture I don't see any significant change in how you value the euro," he added.
If there were another election in Germany, the far-right, anti-immigrant Alternative for Germany (AfD) party could add to the 13 percent of votes it secured in September. But the parliamentary process required to get through another election is considered to be quite difficult, involving more than one vote in the German parliament.
The dollar had also sold off against the yen - generally sought at times of uncertainty - in Asian trading, dipping to a one-month low. But it turned higher against the Japanese currency in European trading, up 0.1 percent at 112.14 yen.
The euro fell as much as 0.5 percent against the dollar in Asian trading to $1.1722, pulling away from a one-month high of $1.1862 set on Wednesday last week. But it recovered to trade flat on the day at $1.1789 in London trade.
"There's no panic in the market at all - it's really a European story," she added. "We're not seeing a broad risk-off move here," said Commerzbank currency strategist Esther Reichelt, in Frankfurt.
Bitcoin was trading at just above $8,000, after hitting a record high of $8,087 on the Luxembourg-based Bitstamp exchange on Sunday.
Many analysts expect this to be a relatively calm week of trading, with US markets closed for the Thanksgiving holiday on Thursday and with few major data releases.