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Sep. 3, 2014, 4:31 PM GMT / Updated Sep. 3, 2014, 4:31 PM GMT

NOVOAZOVSK, Ukraine - Pro-Russian rebels conquering territory in eastern Ukraine are fighting under a new flag that betrays their - and perhaps the Kremlin’s - soaring ambitions. The blue cross set on a red background, which is stitched into uniforms and flies on tanks, represents Novorossiya or 'New Russia' - a notional state that would swallow southern and eastern Ukraine.

It is slowly replacing the disparate flags representing individual independence-minded groups in the regions of Donetsk. Indeed, the separatist regional administration flag in central Donetsk – one of the rebel headquarters – is now flying the Novorossiya flag.

The fighters’ ambitions mirror the flag’s reach.

A rebel commander who recently captured a key town on the road leading to the strategically important town of Mariupol said his men were not about to lay down their arms in a cease-fire, as was reported earlier. They also planned to go as far as the city of Lviv, which lies even further west than Ukraine’s capital, Kiev.

“During [World War II] we freed the territory of the Soviet Union and we went further to Berlin,” said the commander, who calls himself “Gyurza” and whose men now fight under the Novorossiya flag. “Our aim is Lviv.”

His declaration followed conflicting statements from Kiev and Moscow, with the Ukrainian government at one point saying it had reached a "permanent cease-fire" with Russian President Vladimir Putin, which was denied by Moscow.

Putin later suggested that an agreement "to end the bloodshed" could be reached as early as Friday, which Ukraine's prime minister shot down, saying the Russian leader was simply trying to avoid further European and American sanctions.

Whatever his plans for a cease-fire or truce, Putin himself has been using the term Novorossiya to describe the part of Ukraine that Russia controlled during the 19th century for months.

On Friday, Putin addressed the militia of Novorossyia, and praised their "major success" inside Ukraine in a statement on the Kremlin’s website.