* Trying to clinch "grand coalition" deal by Sunday night
* But talks on difficult tie-up could go on longer
* Merkel wants fourth term as conservative chancellor
* SPD wary after previous coalition cost it votes (Adds details on agriculture agreement)
BERLIN, Feb 3 (Reuters) - German Chancellor Angela Merkel's conservatives and the Social Democrats (SPD) sought to resolve disputes on healthcare and labor rules on Saturday during talks to form a government more than four months after an election.
The two camps aim to seal a deal to renew the "grand coalition" that has governed Europe's largest economy since 2013 by the end of Sunday, although some politicians say they could run into Monday or Tuesday.
SPD deputy Manuela Schwesig urged the conservatives to compromise on abolishing fixed-term contracts for workers and reforming Germany's public-private healthcare system.
"I don't think Mrs Merkel can explain why there can't be any movement there," she said as she arrived for talks.
The SPD wants to prove to its skeptical members that it would be able to push through those core policies in the role of junior partner to make another "grand coalition" more appealing.
Many of the SPD's 443,000 members - who will get the chance to vote on any coalition deal - would prefer to revamp the party in opposition rather than another alliance with Merkel after suffering their worst post-war election result in September.
As a compromise, the conservatives have offered to ban the repeated renewal of fixed-term contracts but they do not want to prevent employers from using them. The parties are still working on the topic.
The two camps made some progress on labor policy on Friday by agreeing that employees in companies with more than 45 employees should have the right to move seamlessly back and forth between full- and part-time work.
Healthcare is a big stumbling block and party sources said Merkel and her Bavarian ally Horst Seehofer discussed the issue before meeting with the SPD.
The conservatives reject replacing the current system with a "citizen's insurance" as called for by the SPD and talks are now expected to focus on improving the position of those with public healthcare such as by changing billing rules for doctors, who earn more by treating private patients.
In a sign they are getting closer to a deal, the parties reached an accord on energy and environment, agreeing to set legally binding climate targets for sectors like energy, transport, agriculture and construction to reach by 2030.
Environment Minister Barbara Hendricks said national climate targets for 2020 would not be quite reached but the new targets, which would be written into law in 2019, would ensure Germany can remain a "climate protection pioneer."
They also agreed on agriculture, saying they wanted to put an end to the use of weedkiller glyphosate as quickly as possible and ban the cultivation of genetically modified plants.
In a full day of negotiations, the parties were also hoping to tick off issues including finances, rents and real estate prices and municipalities.
They reached a deal on migration on Friday, agreeing to stick to the wording of January's coalition blueprint that said the parties did not expect annual migration to exceed 220,000 per year.
But the two were still wrangling over its meaning on Saturday, with Joachim Herrmann - a member of Merkel's CSU Bavarian allies who have called for an upper limit - telling Rheinische Post his party had secured a migrant cap.
Meanwhile, SPD deputy Ralf Stegner insisted the number is merely a prediction, writing on Twitter: "The fact remains that the SPD has not agreed to any upper limit and will not do so."
Migration is a sensitive issue given the influx of more than a million migrants since mid-2015 and the conservatives' subsequent loss of support to the anti-immigrant Alternative for Germany (AfD) in September's national election. (Additional reporting by Sabine Siebold; writing by Michelle Martin; editing by Mark Heinrich and Alexander Smith)