The talks, delayed due to the late arrival in Geneva of Russian ambassadors Felix Kovalev and Gennady Fedossov, now were scheduled to end Friday, a UN spokeswoman said.
Edouard Brunner, the Swiss ambassador to France who is currently serving as UN envoy on Abkhazia, will be chairing the talks between the two regions.
A UN statement said Brunner began preparing a "working document" Monday on political and constitutional issues with Russia's delegates and Vicenzo Manno, ambassador of the Conference on Security and Cooperation in Europe.
The draft text is to be presented to the two parties Wednesday.
Jaba Ioseliani is to head Georgia's delegation and Sokrat Jingjolia is to lead the Abkhaz team.
Abkhazian separatist forces, backed by North Caucasian mercenaries and armed covertly by Russian military units, threw off Georgian rule last September.
Their actions were the result of a conflict in which hundreds were killed and tens of thousands made homeless.
The UN High Commission for Refugees said Friday it hoped the fresh talks would pave the way for the start of a stalled repatriation program for an estimated 250,000 ethnic Georgians who fled the breakaway province last year.
About 2,500 Russian peacekeepers are deployed along a zone which runs on either side of the Inguri river.
The river separates Georgia from the lush Black Sea province.
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