The insurgents' platform, released at the start of yesterday's negotiations in Minsk, the Belarusian capital, represented a significant change in their vision for the future of Ukraine's eastern, mainly Russian-speaking region.
It remains unclear, however, whether the talks can reach a compromise amid the brutal fighting that has continued in eastern Ukraine.
Yesterday, the rebels pushed Ukrainian government forces from an airport near Luhansk, the second-largest rebel-held city, the latest in a series of military gains.
The negotiations involve former Ukrainian President Leonid Kuchma; Russia's ambassador to Ukraine; an envoy from the Organisation for Security and Cooperation in Europe and representatives of the rebels.
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Yet similar talks earlier this summer produced no visible results.
Unlike the previous rounds, this time rebels said in a statement carried by Russia's state-run RIA Novosti news agency that they are willing to discuss "the preservation of the united economic, cultural and political space of Ukraine."
In return, they demanded a comprehensive amnesty and broad local powers that would include being able to appoint their own local law enforcement officials.
The talks lasted for several hours yesterday and were adjourned until Friday, when the parties are to discuss a cease-fire and an exchange of prisoners, rebel negotiator Andrei Purgin said, according to RIA Novosti.
The rebels' more moderate negotiating platform appeared to reflect Putin's desire to make a deal that would allow Russia to avoid more punitive Western sanctions while preserving a significant degree of leverage over its neighbour.
A NATO summit in Wales on Thursday is also expected to approve measures designed to counter Russia's aggressive actions in Ukraine.