Ukrainian President Volodymyr Zelensky has called again for a meeting with Russian leader Vladimir Putin in an effort to "put an end to the war".
"I think that whoever started this war will be able to end it," he told a news conference at a metro station in the heart of the Ukrainian capital, adding that he was "not afraid to meet" Mr Putin if it would lead to a peace deal between Russia and Ukraine.
"From the beginning, I have insisted on talks with the Russian president," he said. "It's not that I want (to meet him), it's that I have to meet him so as to settle this conflict by diplomatic means.
"We have confidence in our partners, but we have no confidence in Russia," he added.
Mr Zelensky also criticised a decision by UN Secretary General Antonio Guterres to visit Moscow on Tuesday, before heading to Kyiv.
"It is simply wrong to go first to Russia and then to Ukraine. There is no justice and no logic in this order," he added.
Mr Zelensky also repeated his warning that Ukraine would break off talks if Russia killed the remaining Ukrainian soldiers in the besieged Black Sea port of Mariupol.
"If our men are killed in Mariupol and if these pseudo-referendums are organised in the (southern) region of Kherson, then Ukraine will withdraw from any negotiation process," he said.
He was ready to exchange Ukraine's soldiers defending the city "in whatever format" to save "these people who find themselves in a horrible situation, surrounded".
The "last contact" with the Mariupol soldiers had been an hour before the briefing, he said, adding "today is one of the hardest days" since the start of the Russian siege of the city at the beginning of March.
Ukrainian officials said earlier that Russian forces had resumed their assault on the last Ukrainian defenders holed up in a giant steel works in Mariupol, just days after Moscow declared victory there and said its forces did not need to take the plant.
Russian forces were hitting the Azovstal complex with airstrikes and trying to storm it, Ukrainian presidential adviser Oleksiy Arestovych said, adding "the enemy is trying to strangle the final resistance of Mariupol's defenders".
The biggest battle of the conflict has raged for weeks as Russia seeks to capture a city seen as vital to its attempts to link the eastern Donbas region with Crimea, the Black Sea peninsula that Moscow seized in 2014.
Two missiles struck a military facility and two residential buildings in the Black Sea port city of Odesa, and two more were destroyed, the southern air command of the Ukrainian armed forces said. Ukrainian presidential aide Andriy Yermak said five people had been killed and 18 wounded.
The death toll could not be independently verified. The last big strike on or near Odesa was in early April.
"The only aim of Russian missile strikes on Odesa is terror," Ukrainian Foreign Minister Dmytro Kuleba said on social media. Russia has denied targeting civilians in its "special military operation" that began on 24 February.
A Russian general, Rustam Minnekayev, said on Friday Moscow wanted control of the whole of southern Ukraine, not just Donbas. Ukraine said the comments indicated Russia had wider goals than its declared aim of demilitarising and "denazifying" the country. Kyiv and the West call the invasion an unjustified war of aggression.
Russian forces have besieged and bombarded Mariupol since the early days of the war, leaving a city that is usually home to more than 400,000 people in ruins. A new attempt to evacuate civilians failed earlier today, an aide to Mariupol's mayor said.
Russia's defence ministry said on Friday Mariupol's last fighters had been "securely blockaded" at the steel plant. On Thursday, Mr Putin had declared the city "liberated", declaring that troops would not storm Azovstal.
Mr Arestovych, a political adviser to Mr Zelensky, said Ukrainian troops in the Azovstal complex were still holding out "despite the very difficult situation" and were attempting counterattacks. More than 1,000 civilians are also in the plant, according to Ukrainian authorities.
The Azov battalion, a nationalist militia prominent in the defence of Mariupol, released a video which it said showed women and children sheltering in the complex. Reuters could not independently verify where or when the video was shot.
One unnamed boy in the video said he was desperate to get out after being in the bunker for two months.
"I want to see the sun because in here it's dim, not like outside. When our houses are rebuilt we can live in peace. Let Ukraine win because Ukraine is our native home," he said.
Ukraine estimates tens of thousands of civilians have been killed in Mariupol and says 100,000 civilians are still there. The United Nations and Red Cross say the civilian toll is at least in the thousands.
Russia's current offensive is focused on Donbas, where Moscow-backed separatists have for years held parts of its constituent Donetsk and Luhansk regions.
Earlier, Luhansk governor Serhiy Haidai said Ukrainian forces were pulling back from some settlements to new defensive lines to preserve their units in the face of an intensifying barrage on all cities in the region.
The governor of Kharkiv, a heavily bombarded city northwest of Donbas, said Russian forces had carried out over 50 artillery or rocket attacks in the area over the past day, killing two people and wounding 19.
Governor Oleh Synegubov said intense fighting continued at the frontline town of Izyum, southeast of the city, and that Ukrainian forces had retaken three villages to its northwest.
Russia said it had shot down a Ukrainian fighter jet and destroyed three Ukrainian helicopters at an airfield in Kharkiv.
There was no immediate comment from Ukraine on the Russian assertion. The Ukrainian military said today it had destroyed 177 Russian aircraft and 154 helicopters since the start of the war. Reuters could not verify the figures.
Russian forces made no big gains in the last 24 hours, British military intelligence said early this morning.
General Minnekayev, deputy commander of Russia's central military district, was quoted by Russian news agencies as saying full control over southern Ukraine would give Russia access to Transdniestria, a breakaway Russian-occupied part of Moldova.
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Mr Zelensky said after the general's comments that Russia's invasion was just the beginning and that Moscow has designs on other countries.
"We are the first in line. And who will come next?" he said in a video address late last night.
Kremlin spokesman Dmitry Peskov declined comment on whether Russia had expanded its goals.
Mr Zelensky also said Ukraine's allies were finally delivering weapons Kyiv has asked for.
Meanwhile, the Organization for Security and Cooperation in Europe said today it was trying to secure the release of a number of Special Monitoring Mission (SMM) staff members who had been detained in eastern Ukraine.
"The OSCE is extremely concerned that a number of SMM national mission members have been deprived of their liberty in Donetsk and Luhansk. The OSCE is using all available channels to facilitate the release of its staff," its media office said.
