The failure on Friday raised the pressure on Merkel and Schroeder to resolve their rival claims to the chancellorship and end the political drift threatening Europe's most populous country.
Fronted by Merkel, the conservatives defeated Schroeder's Social Democrats in Sunday's parliamentary vote. But they fell short of a majority for her programme of accelerated economic reforms.
Merkel, head of the Christian Democratic Union, held talks on Friday morning with Greens leaders to sound out whether they could ally with her and the pro-business Free Democrats.
German media have labelled the improbable alliance the "Jamaica coalition" because the three parties' official colors -black, yellow and green- resemble those of the Caribbean nation's flag.
But the Greens - junior partners in Schroeder's outgoing government coalition - killed speculation they could lurch to the right, citing wide disagreements on policy issues.
"The differences are very big," Merkel told reporters after the talks near the Reichstag parliament building. "I would have liked to have spoken more in detail about where we overlap, but the Greens have a different wish."
Greens party co-chairman Reinhard Buetikofer said he challenged Merkel and Edmund Stoiber, leader of the Bavaria-only Christian Social Union, to explain whether they would drop their "neo-liberal, radical market, anti-ecological policies".
"I would have liked to have spoken more in detail about where we overlap, but the Greens have a different wish"
Christian Democratic Union
"Mrs Merkel and Mr Stoiber didn't give us the answer, and on that basis we said we see no possibility to recommend further talks," Buetikofer said.
Greens leaders have cited Merkel's plans to keep German nuclear power stations open longer and her rejection of Turkish membership in the European Union as major stumbling blocks.
Just as the Greens are resisting the advances of the conservatives, so the Free Democrats have snubbed overtures from Schroeder's party, narrowing the leaders' room for manoeuvre.
The Social Democrats have also ruled out any form of cooperation with the Left Party, a new bloc of former East German communists and renegade Social Democrats who call for Schroeder's welfare reforms to be reversed.
With both Merkel and Schroeder ruling out a minority government, many observers believe a so-called "grand coalition" of their two parties will emerge after weeks of wrangling.
The two held brief initial talks on Thursday and agreed to meet again next week.
Schroeder (L) has been meeting
SDP leader Muentefering
Both said Germany needed a government stable enough to carry out further reforms to a cherished welfare state system creaking under the burden of a weak economy and an ageing population. But it remained unclear how they would reconcile their rival claims to lead a new administration.
Some observers, including a former Social Democrat chairman, have forecast that both would have to step down.
Others suspect Schroeder of trying to engineer another election.
Schroeder argues that German voters rejected Merkel as chancellor, awarding her Christian Democratic Union only 27.8% support after months of polling as much as 40%.
However, including the Christian Social Union, the conservatives reached 35.2%, topping the Social Democrats' 34.3%.
Whoever triumphs, there is little prospect of a radical overhaul of the welfare state or its consensus-based political and economic system.
"Both major parties campaigned on economic and social reform and lost," the Sueddeutsche Zeitung said in an editorial on Friday. "In this parliament, only a pragmatically identified core of reforms can be realised."