* 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
* Officials offer conflicting views on peace negotiations
By Hamuda Hassan, Jorge Silva and Natalia Zinets
DOBROPILLIA, Ukraine/KYIV, May 1 (Reuters) - Russia carried out missile strikes across southern and eastern Ukraine on Saturday, Ukrainian officials said, and some women and children were evacuated from a steel plant in the besieged city of Mariupol after sheltering there for over a week.
Moscow has turned its focus toward 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 in the south, giving them a foothold just 100 km (62 miles) north of Russian-annexed Crimea, and have mostly occupied Mariupol, a strategic eastern port city on the Azov Sea.
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, and 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 4 square km plant.
Palamar said both Russia and Ukraine were respecting a local ceasefire, and that he hoped the evacuated civilians would be transferred 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, according to Ukrainian officials.
To the west in Odesa, which has so far been relatively unscathed in the war, a Russian missile launched from Crimea destroyed the runway at the main airport, said Maksym Marchenko, Odesda's regional governor. No one was hurt, he added.
Ukraine's military said the airport could no longer be used. Volodymyr Zelenskiy, Ukraine's president, vowed in a late-night video address to rebuild the airport, adding: "Odesa will never forget Russia's behavior towards it."
There was no comment on the strike from Moscow, whose forces have sporadically targeted Odesa, Ukraine's third-largest city. Eight people were killed in a Russian strike on the city last week, Ukrainian officials said.
Moscow's assault in the south is aimed in part at linking the area with Crimea as it pushes for complete control over Ukraine's eastern Donbas region. Parts of Donbas' two provinces, Luhansk and Donetsk, were already controlled by Russian-backed separatists before Moscow's Feb. 24 invasion.
In his address, 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."
PEACE TALKS
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.
Russian Foreign Minister Sergei Lavrov said lifting Western sanctions on Moscow was part of the negotiations, but senior Ukrainian negotiator Mykhailo Podolyak denied this was the case.
Ukraine's president, Volodymyr Zelenskiy, insists sanctions need to be strengthened and cannot be negotiated upon. He warned on Friday that talks could collapse due to what he called Russia's "playbook on murdering people".
Ukraine accuses Russian troops of carrying out atrocities as they withdrew from areas near Kyiv in early April. Moscow denies the claims. Negotiators last met face-to-face on March 29, and have since spoken by video link.
The United States and its European allies have imposed sweeping sanctions on Russia's economy and provided Ukraine with weapons and humanitarian aid.
U.S. President Joe Biden is seeking a $33 billion aid package for Kyiv, including $20 billion for weapons, and British Prime Minister Boris Johnson said on Saturday his country would continue "to give the Ukrainians the equipment they need to defend themselves."
Lavrov said that if Washington and its partners in the U.S.-led NATO military alliance truly wanted to resolve the crisis, they should stop sending weapons to Kyiv.
'EVERYTHING IS DESTROYED'
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.
One resident, who gave only his first name of Andriy, said his partner was in a room facing the yard at the time of the attack and was knocked unconscious.
"Thank God the four children were in the kitchen," he said, standing in the destroyed living room.
Residents sifted through their belongings to see what could be salvaged.
"At around 9:20 a.m. this happiness flew to our house," another resident, Oleh, said sarcastically. "Everything is destroyed."
Russia reported more Ukrainian strikes on its territory on Saturday.
Officials in Russia's Bryansk region, which borders Ukraine and Belarus, said air defences had prevented a Ukrainian aircraft from entering. The resulting shelling had hit parts of a Russian oil terminal, they said.
South of Bryansk in the Russia's Kursk region, also on the Ukrainian border, several shells were fired from Ukraine toward a Russian checkpoint, Kursk Governor Roman Starovoit said. There were no casualties or damage, he added.
Ukraine has not directly claimed responsibility for a spate of such incidents on Russian territory. But it described a series of blasts in Russia's south on Wednesday as payback and "karma" for Moscow's invasion.
(Reporting by Hamuda Hassan and Jorge Silva in Dobropillia, Ukraine, and Natalia Zinets in Kyiv; Additional reporting by Reuters journalists; Writing by Frances Kerry and Rami Ayyub; Editing by Catherine Evans, Hugh Lawson and Daniel Wallis)
