* Moscow steps up assault in Ukraine's south, eastern Donbas

* 20 civilians evacuated from Mariupol steel plant

* Odesa airport, Luhansk and Donetsk hit with missiles

DOBROPILLIA/KYIV, Ukraine, May 1

Ukraine's shelling killed and injured its own civilians in the southern region of Kherson, Russia said on Sunday, after pounding southern and eastern areas with missile strikes, while some civilians got away from a steel plant in besieged Mariupol.

Moscow has turned its focus to Ukraine's south and east after failing to capture the capital Kyiv in a nine-week assault that has flattened cities, killed thousands of civilians and forced more than 5 million to flee abroad.

Its forces have captured the town of Kherson, giving them a foothold just 100 km (60 miles) north of Russian-annexed Crimea, and have mostly occupied Mariupol, the strategic eastern port city on the Azov Sea.

Russia's defence ministry accused Ukraine's forces of shelling a school, kindergarten and cemetery in the villages of Kyselivka and Shyroka Balka in the Kherson region, the Russian RIA news agency said on Sunday.

The ministry gave no further details. There was no immediate response from Ukraine to the report, which Reuters could not independently verify.

Russia declared victory in Mariupol on April 21, even as hundreds of Ukrainian troops and civilians took shelter in the Azovstal steel works.

The United Nations has urged an evacuation deal. On Saturday a Ukrainian fighter inside said some 20 women and children had made it out.

'We are getting civilians out of the rubble with ropes - it's the elderly, women and children,' said the fighter, Sviatoslav Palamar, referring to wreckage within the plant, which sprawls 4 sq km (1.5 sq miles).

Palamar said Russia and Ukraine were respecting a local ceasefire, and he hoped the evacuated civilians would be taken to the Ukrainian city of Zaporizhzhia to the northwest.

There was no comment from Russia or the United Nations on the evacuations. Hundreds of Ukrainians remain inside the steel works, Ukrainian officials say.

ODESA STRIKE

A Russian missile launched from Crimea destroyed the runway at the main airport in the city of Odesa to the west, said regional governor Maksym Marchenko, but no one was hurt.

The airport could no longer be used, Ukraine's military said. President Volodymyr Zelenskiy vowed to rebuild it, saying in a late-night video speech, 'Odesa will never forget Russia's behaviour towards it.'

There was no comment on the strike from Moscow, whose forces have sporadically targeted Ukraine's third-largest city, where eight people were killed in a recent Russian strike, Ukrainian officials said.

Moscow's assault in the south aims in part to link the area with Crimea as it pushes for complete control of Ukraine's eastern Donbas region, where Russian-backed separatists already controlled parts of Luhansk and Donetsk provinces before Moscow's Feb. 24 invasion.

In his speech, Zelenskiy said Russia was 'gathering additional forces for new attacks against our military in the east of the country' and 'trying to increase pressure in the Donbas'.

Moscow calls its actions a 'special operation' to disarm Ukraine and rid it of anti-Russian nationalism fomented by the West. Ukraine and the West say Russia launched an unprovoked war of aggression.

Despite weeks of peace talks, both sides looked to be as far apart as ever on Saturday.

Ukraine accuses Russian troops of carrying out atrocities in areas near Kyiv in early April, a claim denied by Moscow. Negotiators last met face-to-face on March 29, and have since spoken by video link.

'EVERYTHING IS DESTROYED'

The United States and its European allies have imposed sweeping sanctions on Russia's economy and supplied Ukraine with weapons and humanitarian aid.

Britain will continue 'to give the Ukrainians the equipment they need to defend themselves', Prime Minister Boris Johnson said on Saturday.

U.S. President Joe Biden is seeking a $33 billion aid package for Kyiv, including $20 billion for weapons.

Biden praised the courage of journalists covering the Russian invasion of Ukraine in comments at the White House Correspondents' Association dinner in Washington.

'A poison is running through our democracy... with disinformation massively on the rise,' Biden said on Saturday night. 'You, the free press, matter more than you ever did in the last century.'

Britain's Foreign Office warned on Sunday that Russia was using a troll factory to spread disinformation about the war in Ukraine on social media.

'We cannot allow the Kremlin and its shady troll farms to invade our online spaces with their lies about Putin's illegal war,' Foreign Secretary Liz Truss said in a statement.

In the town of Dobropillia in Donetsk, the shockwave from a strike on Saturday blew in the windows of an apartment building and left a large crater in the yard.

Standing in his living room, a resident who gave only his first name, Andriy, said his partner was knocked unconscious. 'Thank God the four children were in the kitchen,' he said.

People sifted belongings to salvage what they could.

'At around 9:20 a.m. this happiness flew to our house,' said another resident, Oleh, sarcastically. 'Everything is destroyed.'

Russia reported more Ukrainian strikes on its territory.

Officials in the Bryansk region, which borders Ukraine and Belarus, said air defences had kept out a Ukrainian aircraft, but the resulting shelling hit parts of a Russian oil terminal.

South of Bryansk, in Kursk, another border region, several shells were fired from Ukraine toward a Russian checkpoint, said the regional governor, Roman Starovoit, but with no casualties or damage.

Ukraine has not claimed responsibility for such incidents but it described a series of blasts in Russia's south on Wednesday as payback and 'karma' for Moscow's invasion.