* 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)
BERLIN, Feb 3 (Reuters) - German Chancellor Angela Merkel's conservatives and the Social Democrats (SPD) reached agreement on energy and agriculture on Saturday, but were still in dispute over healthcare during talks to form a government, more than four months after the election.
The two camps aim to seal a deal by the end of Sunday to renew the "grand coalition" that has governed Europe's largest economy since 2013, 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 sceptical 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 to vote on any coalition deal - would prefer their party to revamp in opposition rather than join another alliance with Merkel after suffering their worst post-war election result in September.
Healthcare is a big stumbling block and party sources said Merkel and her Bavarian ally Horst Seehofer discussed the issue before meeting 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.
The parties are not expected to come to an agreement on the most controversial issues, which include healthcare and labour market policy, until the near the end of negotiations.
The conservatives have offered to ban the repeated renewal of fixed-term contracts but do not want to prevent employers from using them as the SPD demands.
The two camps made some progress on labour policy on Friday by agreeing that employees in companies with more than 45 workers should have the right to move seamlessly back and forth between full- and part-time employment.
ENERGY AND FARMING
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.
The parties are hoping to tick off issues like finances, home building and rents during negotiations.
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 blocs 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 the 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 Andrew Bolton)