Leonid Slutsky added the delegations could soon reach draft agreements.

Mr Slutsky said: "According to my personal expectations, this progress may grow in the coming days into a joint position of both delegations, into documents for signing."

The development comes after Ukrainian negotiator and presidential adviser Mykhailo Podolyak also said on Sunday that he thought progress could be made in the negotiations in the coming days.

He added that the Russian side had become more constructive.

Ukraine has previously said it is willing to negotiate, but not to surrender or accept any ultimatums.

Ukraine war: Putin's forces strike base 15 miles from NATO territory - follow live updates

"We will not concede in principle on any positions. Russia now understands this. Russia is already beginning to talk constructively. I think that we will achieve some results literally in a matter of days," he said in a video posted online.

Mr Podolyak also said Ukraine is working with Israel and Turkey as mediators to finalise a location and framework for peace negotiations with Russia.

"When it is worked out, there will be a meeting. I think it won't take long for us to get there," he said on national television.

Three rounds of talks between the two sides in Belarus, most recently last Monday, have focused mainly on humanitarian issues and led to the limited opening of some corridors for civilians to escape fighting.

Russian President Vladimir Putin said on Friday there had been some "positive shifts" in the talks, but did not elaborate.

On Saturday the Kremlin said the discussions between Russian and Ukrainian officials had been continuing "in video format".

In other developments:

• Thirty-five people killed after Ukrainian base used for NATO drills is hit by strikes
• Pope tells Putin "in the name of God I ask you, stop this massacre"
• Putin's potential use of nuclear weapons a concern for UK government, Gove says
• Ukraine working with Israel and Turkey as mediators for peace talks with Russia
• Russia 'installs new mayor in Ukrainian city of Melitopol'
• Britons who host refugees will get £350-a-month 'thank you' from the government
• Award-winning American film-maker killed in Ukraine

The possible breakthrough comes after thirty-five people were killed in a Russian airstrike on a Ukrainian military base used for NATO drills less than 15 miles from the Polish border, the governor of the Lviv region said.

Maksym Kozytskyy also said 134 people were injured after 30 cruise missiles were fired at the International Centre for Peacekeeping and Security in Yavoriv, in what appears to be the westernmost attack of the war so far.

The strike has taken the war close to the border of Poland, a member of NATO, after a senior Russian diplomat warned that Moscow considers Western shipments of military equipment to Ukraine "legitimate targets" for attacks.

Ukraine's defence minister Oleksii Reznikov has said foreign military instructors work on the military training site in the Lviv region.

A defence ministry representative said they are still trying to establish if any of the instructors were at the facility at the time of the attack.

Reuters says a witness saw more than a dozen ambulances heading in the direction of the base.

US national security adviser Jake Sullivan warned that if Russia "takes a shot on" NATO territory, the bloc would respond with its "full force".

Mr Sullivan said it would trigger NATO's Article 5, which says an attack on one NATO ally would be considered an attack on all allies.

"If there is a military attack on NATO territory it would cause the invocation of Article 5, and we would bring the full force of the NATO alliance to bear in responding to it," he told CBS.

Since 2015, the US has regularly sent instructors to the site and the facility has also hosted international NATO drills.

The military training facility is the biggest in western Ukraine and is located less than 15 miles (25km) from the border with Poland.

Russia warned they face a 'fight to the death' to take Kyiv

Russian fighters have also fired at the airport in Ivano-Frankivsk, a city in western Ukraine located 155 miles (250km) from the border with Slovakia and Hungary.

Mayor Ruslan Martsinkiv said Russia's goal is "to sow panic and fear".

The attacks come after Ukrainian President Volodymyr Zelenskyy warned Russian forces that they face a fight to the death if they try to occupy the capital Kyiv.

"If they decide to carpet bomb and simply erase the history of this region... and destroy all of us, then they will enter Kyiv. If that's their goal, let them come in, but they will have to live on this land by themselves," Mr Zelenskyy said on Saturday.

Read more: Trump says Putin will only get worse - latest updates on Ukraine

Russia 'trying to create breakaway republic in Kherson'

In his nightly address on Saturday, President Zelenskyy also warned Russia was trying to make the captured city of Kherson a breakaway republic similar to Donetsk and Luhansk in eastern Ukraine.

"The invaders in the Kherson region are trying to repeat the notorious experience of the formation of pseudo-republics," he said.

"Blackmail local leaders, put pressure on deputies, look for someone to bribe. They're trying to organise the so-called 'KPR' (Kherson People's Republic)... against the will of the people who go out to protest every day, and who want Ukraine."

He added during the speech: "Ukraine will stand this test. We need time and strength to break the war machine that has come to our land."

The Ukrainian president also said 1,300 Ukrainian soldiers had died since the Russian invasion began on 24 February.

Mr Zelenskyy also once again criticised NATO's refusal to declare a no-fly zone over Ukraine and said his country has sought ways to procure air defence assets, though he did not elaborate.

NATO has said imposing a no-fly zone could lead to a wider war with Russia.

US President Joe Biden has announced another $200m (£153m) in aid to Ukraine, with an additional $13bn (£10bn) included in a bill that has passed the House of Representatives and should pass the Senate within days.

Russia 'installs new mayor' and continues to bombard cities

On Saturday, the Ukrainian parliament claimed Russia has installed a new mayor in the southern port city of Melitopol - a day after the city's elected mayor was allegedly kidnapped by forces.

Galina Danilchenko, a former member of the city council, was announced as the new mayor on local TV, according to reports.

Ukraine's parliament claimed that the previous mayor, Ivan Fedorov, was kidnapped by armed men acting on behalf of the Kremlin on Friday.

Russia has continued to bombard cities across Ukraine over the weekend, pounding Mariupol in the south, shelling the outskirts of Kyiv and thwarting the efforts of people trying to flee the violence.

In Mariupol, which has endured a 12-day blockade, efforts to take food, water and medicine into the port city and to evacuate civilians were prevented by unceasing attacks.

Russian soldiers pillaged a humanitarian convoy that was trying to reach Mariupol and blocked another, a Ukrainian official said.

More than 1,500 people have died in Mariupol during the siege, according to the mayor's office, and the shelling has even interrupted efforts to bury the dead in mass graves.

A satellite image released by Maxar Technologies shows buildings on fire in the Primorskyi district of western Mariupol as Russia attacks the city.

Two other satellite images show apartment buildings in Mariupol before and after the Russian invasion.

Meanwhile, the British government has revealed details of a new scheme to help people fleeing the Russian invasion as the UK's ambassador to Ukraine said she "totally gets the criticism" of the refugee system to date.

The Homes for Ukraine programme, to be rolled out this week, will allow individuals, charities, community groups and businesses to bring people escaping the war to safety - even if they have no ties to the UK.

Britons offering accommodation to Ukrainian refugees through the new route will receive a "thank you" payment of £350 per month.