The situation is an untenable mess for both sides – a lasting solution may yet be found at the negotiating table

As the conflict in eastern Ukraine enters its nastiest phase yet, with reports of a convoy of refugees coming under fire on Monday and civilian casualties increasing by the day, there are signs that both Moscow and Kiev are looking for a way out. What is unclear, however, is whether there is any compromise to be found that would be acceptable to both capitals.

Russia's aid to the rebels has hardly stopped: just last week the prime minister of the self-declared Donetsk People's Republic claimed to have received 1,200 fighters from Russia who had spent four months undergoing training across the border. Ukraine, meanwhile, is only strengthening the rhetoric about bringing the "anti-terrorist operation" in the east of the country to a victorious end, not put off by the increasing civilian casualties.

Dozens of people, including women and children, were reported to have been killed on Monday when the convoy carrying refugees was hit by rocket fire near the eastern city of Luhansk, a Ukrainian military spokesman said. Government forces and pro-Russia rebels were quick to accuse each other of the attack on the vehicles, which were evacuating civilians from the towns of Khryaschuvate and Novosvitlivka.

But despite the developments on the ground, there is the unmistakable sense that something is going on behind the scenes. A number of rebel leaders, including the top commander Igor Strelkov, have been pulled out, perhaps back to Russia. Strelkov was "going on holiday" according to others in the rebel movement, while other leaders have simply disappeared.

The remaining leaders appear to have gone into a surreal "end of days" mode. One leading rebel said in an interview with a Russian newspaper recently that possibly neither Strelkov nor any of the other rebels actually existed, and probably everyone was simply living in an alternative reality like that portrayed in the film The Matrix.

Meanwhile on Monday, the rebels officially introduced the death penalty in areas they control. Shelling and street battles have come close to the city centres of both Donetsk and Luhansk.

At the same time, cautious diplomatic channels have opened over the heads of the rebel leaders on the ground.

The heads of the Russian and Ukrainian presidential administrations met in the Black Sea city of Sochi on Friday, especially significant because the Russian head is Sergei Ivanov, a leading Kremlin hawk and very close to Vladimir Putin. Little is known of what they discussed, but that meeting paved the way for Sunday's five-hour talks between the two countries' foreign ministers in Berlin, where they were joined by their French and German counterparts.

The talks do not seem to have borne much fruit. Ukraine's Pavlo Klimkin wrote on Twitter that the country had refused to cross "red lines", suggesting that Russia's offer of compromise involved concessions unacceptable to Kiev. Russia's Sergei Lavrov said there was not much point in talks without the declaration of a ceasefire.

Kiev is unlikely to agree to this given it has made serious gains against the rebels in recent weeks and has pushed them into the two strongholds of Donetsk and Luhansk. The Ukrainian authorities feel they are close to defeating the insurgency and would not want to give the rebels time to regroup.

Lavrov continues to deny that Russia is sending any equipment across the border, and pointed out that an OSCE observer mission placed at border crossing points in the region has not identified any unlawful crossings of the border. However, the mission can only observe official crossings and has no mandate to check the long, unguarded sections of the border where crossings of men and equipment occur frequently.

What is becoming clear is that the Russia-backed rebels cannot win the war with Ukraine without direct Russian intervention. The Ukrainian army is in chaos but has regrouped in recent months and been augmented with controversial volunteer battalions, making it simply too much for the rebels to handle, even with the covert help from across the border. Thus for Russia, the two unappealing choices appear to be to abandon the rebellion entirely or to send in a proper Russian invasion force.

"Behind the rattling sabres, the Russians appear to have stepped up their efforts to reach some diplomatic resolution," wrote Mark Galeotti, a Russia analyst at New York University, in a recent column for Business New Europe magazine.

"Rather than gearing up for an invasion, Moscow is hoping rather to be able to negotiate its way to some face-saving formula which would allow Putin to abandon the increasingly expensive political liability that is [the rebel project] while claiming it as a success."