Russia and Ukraine have accused each other of violating separate ceasefires declared by each side to cover the celebrations of the Soviet Union's victory over Nazi Germany.

The Russian defence ministry reported more than 1,000 violations in the conflict zone, while Moscow's mayor said the city had been targeted by drones since the ceasefire began at midnight local time (21:00 GMT Thursday).

Ukraine also said Russia had continued to strike its positions since that time.

Russian President Vladimir Putin announced a ceasefire for 8-9 May ahead of Victory Day celebrations on Saturday. Kyiv had earlier called for an indefinite truce, starting 6 May.

Russia has warned Ukraine not to try to attack the Victory Day parade in Red Square.

Its defence ministry has threatened to launch a "retaliatory, massive missile strike" on the centre of Kyiv if Moscow is attacked. It has warned foreign diplomats to leave the Ukrainian capital ahead of 9 May.

For the first time in nearly two decades there will be no military hardware at the parade, while the Russian capital is on high alert over the fears that Ukraine could try to disrupt the events.

Residents of Moscow and St Petersburg have also been warned their mobile internet access will be limited for security reasons.

The celebrations used to bring large numbers of foreign guests to Moscow, but this time only the leaders of Belarus, Malaysia and Laos, and a few other dignitaries, will attend.

In a post on Telegram on Friday morning, the Russian defence ministry said there had been 1,365 violations of the ceasefire, including 153 artillery strikes and 887 drone strikes in the conflict zone.

It said Ukraine was also continuing to strike civilian targets in border areas of the Kursk and Belgorod regions, close to the conflict zone.

Russian armed forces provided a "mirror response" to the violations, the ministry added.

Meanwhile Moscow Mayor Sergey Sobyanin said some 20 drones had been downed near the city in just the first two hours of the ceasefire.

Ukrainian strikes were also reported on industrial sites in the Perm and Yaroslavl regions, as well as sites in the Rostov region and the Chechen capital Grozny.

Thirteen airports in southern Russia also suspended operations after a drone attack.

Ukrainian President Volodymyr Zelensky posted on Telegram that there had been more than 140 attacks on Ukrainian positions in the first few hours of the truce, and more than 850 drone strikes.

"All of this clearly indicates that there was not even a simulated attempt from the Russian side to cease fire at the front," he said.

"Just like in the results of the past day, Ukraine will act in kind today."

On Thursday Ukraine accused Russia of breaching Kyiv's unilateral ceasefire, launching drone attacks, including on a kindergarten in Sumy region. Two people were killed in that attack, although no children were present at the time.

The war of words over ceasefires came after European Council President António Costa said he thought there was "potential" for the EU to negotiate with Russia over ending the war, and said they had Zelensky's backing to do so.

"I'm talking with the [EU's] 27 national leaders to see the best way to organise ourselves and to identify what we need effectively to discuss with Russia when it comes to the right moment to do this," he said in an interview with the Financial Times on Thursday.

"We cannot change the geography. We are in Europe, we are neighbours of Russia, and of course we need to talk with them about the future of the security architecture of Europe," he added.

Kremlin spokesman Dmitry Peskov responded that Russia was ready for dialogue but "will not initiate such contacts ourselves".

The US has mediated several rounds of talks between Russia and Ukraine but so far without any breakthrough, and there are concerns that Washington is now distracted by the war in the Middle East.

Speaking on a visit to Italy on Friday, Secretary of State Marco Rubio said the US was still prepared to mediate but did not want to waste time if progress was not being made.

Zelensky said he expected US envoys to come to Kyiv in the next few weeks.

Separately Ukrainian emergency personnel are battling a huge wildfire in the exclusion zone at Chornobyl, known at the time of the nuclear disaster in the former Soviet Union by its Russian name, Chernobyl.

Strong winds, dry weather and landmines in some areas from the ongoing conflict are complicating efforts to control the blaze. Firefighters say it's spreading rapidly - already covering some 11 sq km (4.2sq miles).

The exclusion zone, in the Kyiv region, remains highly contaminated but the authorities say radiation in the area of the fire remains within the normal range.