* Extend talks beyond self-imposed Sunday deadline
* Healthcare, labor policy final stumbling blocks
* Negotiators upbeat on prospects for deal
* Conservatives, SPD reach agreement on Europe (Updates with agreement on Europe)
BERLIN, Feb 5 (Reuters) - Negotiators for German Chancellor Angela Merkel's conservatives and the center-left Social Democrats (SPD) reconvened on Monday to hammer out compromises on healthcare and labor policy, the stumbling blocks in the way of another "grand coalition."
The parties missed a self-imposed Sunday deadline to clinch a deal on renewing the coalition that has governed Europe's largest economy since 2013. But both sides cited progress and said the remaining differences did not appear insurmountable.
"It's going to work out," the SPD's Andrea Nahles said on arrival for Monday's negotiations at her party headquarters. Another SPD negotiator, Karl Lauterbach, put the chances of the parties striking a deal on Monday at 50-50.
The Rheinische Post newspaper, citing an internal SPD schedule, reported that Merkel, the leader of her Bavarian allies Horst Seehofer and SPD chief Martin Schulz wanted to present a final coalition agreement on Tuesday.
But Alexander Dobrindt of the Bavarian Christian Social Union (CSU) said: "The hurdles are still big."
In a sign of progress, the parties concluded their talks on Europe with an agreement to invest more in the euro zone and end austerity, Schulz said.
"Today we have completed the consultations in the field of Europe," he said on social media, adding that the agreement included "more investment, an investment budget for the euro zone and an end of forced austerity!"
The parties further agreed to seek fairer corporate taxation in Europe, including for Internet giants like Google, Apple, Facebook and Amazon.
Schulz made no specific mention in his message, however, of any plans for the European Stability Mechanism (ESM) to become a European Monetary Fund, as was envisaged in a coalition blueprint agreed on Jan. 12 after exploratory talks.
Some conservatives fear that rushing ahead with European integration would create too much of a burden for German taxpayers.
The SPD made reform of the European Union a priority in campaigning for last September's federal election, pledging in its manifesto to work for "a better and fairer Europe."
The message failed to resonate with voters, however, and the SPD slumped to its worst post-war election result.
Now, the party is trying to extract concessions on domestic policy that could win over skeptics among its 443,000 members, who get the final say on whether to move ahead with another tie-up with the conservatives.
Merkel's failure to cobble together a new government more than four months after the election has raised concerns among investors and partner countries at a time when Europe is facing multiple challenges - including the need for euro zone reform and Britain's looming departure from the EU.
Germany could face a new election or an unprecedented minority government if SPD members reject a coalition deal.
EU Budget Commissioner Guenther Oettinger told the Rheinische Post the parties should finalize a coalition deal as soon as possible for the sake of pending EU decisions on asylum, banking and budget matters.
The parties agreed on Sunday to invest more than 2 billion euros in social housing by 2021, to spend up to 12 billion euros on expanding broadband and to channel 33 billion euros to municipalities for investments, including in childcare.
Agreements were also reached on migration, energy and agriculture in recent days.
The SPD regards advances on labor rules and healthcare as crucial to winning over left-wing members and other skeptics.
Conservatives have thus far rejected a push by the SPD to ban short-term employment contracts imposed by employers without justification. But they have offered to prevent the repeated renewal of such short-term employment contracts as a compromise.
The two sides are also at odds over the SPD's call to replace Germany's dual public-private healthcare system with a universal insurance system for all.
Monday's talks were expected to focus on improving public healthcare, such as by changing billing rules for doctors, who earn more by treating privately insured patients. (Editing by Janet Lawrence/Mark Heinrich)