Russian and Ukrainian foreign ministers are meeting in Berlin for the first time in weeks for talks aimed at ending the conflict in eastern Ukraine, where there was heavy fighting over the weekend for control of the city of Luhansk.

The meeting between Pavlo Klimkin of Ukraine and Russia's Sergei Lavrov is being attended by their German counterpart Frank-Walter-Steinmeier and France's Laurent Fabius.

"It is all about finding a roadmap towards a sustainable ceasefire and a framework for effective border controls," Steinmeier said in a statement before the talks. "Only in this way can eastern Ukraine calm down and Kiev continue a national dialogue that appropriately involves the people in the east."

Steinmeier warned that "a simple recipe does not exist". He added: "That is why it is so important in my view that we all sit down at a table at this time."

On his way to the negotiations, Klimkin tweeted: "Flying to Berlin. The talks will not be easy. It is important to stop the flow of weapons and mercenaries from Russia."

Russia has denied any role in supporting separatists in eastern Ukraine, who have been fighting in recent days to maintain control of one of their most important strongholds, Luhansk.

The government in Kiev said on Sunday the separatists had shot down a Ukrainian warplane, but it was not clear what had happened to the pilot. Kiev said the downing of its plane happened as its forces were fighting their way into Luhansk, capturing a rebel-held police station in the Velika Vergunka district.

The Luhansk authorities said the government siege of the city had left it on the brink of a humanitarian catastrophe, cutting off basic provisions, electric power and water. A Russian aid convoy that was supposed to be bringing relief assistance to Luhansk and other separatist enclaves advanced closer to the Ukrainian border amid continuing controversy over its supervision. Ukraine said it would only allow the trucks across the border under the oversight of the International Committee of the Red Cross (ICRC). The ICRC said there were still no sufficient guarantees of safety for the relief convoy from the warring parties.

Kiev has warned that the Russian convoy was part of a ploy to smuggle Russian arms to the rebels. The Guardian reported on Thursday evening that Russian armoured vehicles crossed the border through a gap in a fence but it was unclear where they were heading. The Kiev government said its artillery had destroyed a Russian armoured column on Friday, but that could not be independently confirmed.

In Donetsk, another rebel-held town under sustained government attack, the local separatist leader, Alexander Zakharchenko, posted a video on Saturday in which he claimed that 1,200 fighters and new military equipment were on their way from Russia. He suggested the reinforcements, which he said included tanks, had already crossed the border.

The Berlin meeting was arranged in talks on Friday in Sochi between the heads of the presidential administrations of both Russia and Ukraine. Steinmeier said on Sunday morning that while the humanitarian crisis in eastern Ukraine was the imminent focus of the foreign ministers' talks, "we must not neglect the search for political ways out of the crisis in Ukraine".

The German foreign minister said: "We urgently need new political impetus. Otherwise we run the risk of treading water, or of going backward and re-entering an intensified spiral of escalation."