Russia's defense ministry said its troops would halt hostilities to allow civilians to leave the besieged steel plant Azovstal in Ukraine's port city of Mariupol from 1400 Moscow time (1100 GMT) on Monday.
The ministry said any civilians trapped at the facility could leave in whichever direction they chose.
"Today, the Russian side once again announced the existence of a corridor for civilians to leave Azovstal. This could be believed if the Russians had not destroyed humanitarian corridors many times before," Ukrainian Deputy Prime Minister Iryna Vereshchuk wrote on the Telegram messaging app.
"It is important to understand that a humanitarian corridor opens by the agreement of both sides. A corridor announced unilaterally does not provide security, and therefore is not a humanitarian corridor."
She said Ukraine had "appealed to UN Secretary-General Antonio Guterres to be the initiator and guarantor of the humanitarian corridor from Azovstal for civilians."
Russian forces were continuing on Monday to attack the vast Azovstal steel plant where Ukrainian fighters are holed up in the southern port city of Mariupol, Ukrainian presidential aide Oleksiy Arestovych said.
"The enemy continues to attack our defenses in the area of the Azovstal plant, using aircraft, artillery ... firing with tanks and trying to advance with assault groups, violating the order of their own supreme commander," Arestovych said in a video address.
Five railway stations came under fire in western and central Ukraine the same day, causing an unspecified number of casualties, Ukrainian television quoted state-run Ukrainian Railways as saying.
Oleksander Kamyshin, the company's chief, said the attacks took place in the space of an hour and details were being checked.
Russia also says its air force stuck 56 Ukrainian military infrastructure facilities on Sunday night, according to TASS.
Ukraine's defense ministry said on Monday Russia was continuing to attack in eastern Ukraine but was being pushed back.
Defense Ministry spokesperson Oleksandr Motuzyanyk said Russian forces had attempted to break through the defenses of towns including Rubizhne, Popasna, Sievierodonetsk, Maryinka and Avdiivka, and was attempting to advance from the town of Izyum towards Barvinkove and Sloviansk.
Russia has also begun concentrating troops in the Belgorod Oblast, near the Ukrainian border, Interfax reported, citing Motyzyanyk.
He further added that Russian forces have stationed eight ships armed with cruise missiles in the Black Sea with a total missile volley of 58 missiles, Ukrainian state media outlet Ukrinform reported.
Russia has made minor advances in some areas since shifting its focus to fully occupying Donbas, the UK's Ministry of Defense tweeted in a regular bulletin on Monday.
"Without sufficient logistical and combat support enablers in place, Russia has yet to achieve a significant breakthrough," it said.
Ukraine's defense of Mariupol has also exhausted many Russian units and reduced their combat effectiveness, British military intelligence said.
Russian air defense systems shot down two Ukrainian drones in Russia's Kursk region which borders Ukraine, regional Governor Roman Starovoyt wrote on his Telegram channel on Monday.
He said there were no casualties.
Russia struck Ukraine's Kremenchuk oil refinery the same day with long-range missiles and hit military installations in its former Soviet neighbor, according to the Russian defense ministry.
"High-precision long-range weapons destroyed fuel production facilities at an oil refinery on the northern outskirts of the city of Kremenchuk, as well as petroleum products storage facilities which fueled military equipment for Ukrainian troops," the ministry said.
Russia fired rockets at targets near two towns in Ukraine's central Vinnytsia region on Monday, killing five people and wounding 18, the regional prosecutor's office said.
"Today, Vinnytsia region is once again under rocket fire (in) the towns of Zhmerynka and Kozyatyn. The enemy is attempting to hit critical infrastructure," regional Governor Serhiy Borzov said in a video released on the Telegram messaging app. Russia did not immediately comment on his remarks.
More explosions were heard Monday morning in the Lviv region, Pravda reported. Fires reportedly broke out and residents nearby were urged to stay indoors.
Ukrainian air defenses destroyed a Russian Su-34 aircraft in the Kharkiv region, according to Ukrainian media.
Blinken pledges return of US diplomats and more security, says Russia failing in war aims
Russia is failing in its war aims but Ukraine is succeeding, US Secretary of State Antony Blinken said on Monday after he and Defense Secretary Lloyd Austin met President Volodymyr Zelinsky and Ukrainian officials in Kyiv.
"In terms of Russia's war aims, Russia has already failed and Ukraine has already succeeded," Blinken told a news briefing in Poland after the two officials returned from the meeting, which ran three hours instead of an allotted 90 minutes.
The United States took the opportunity of the first official US visit to Ukraine since Russia's invasion two months ago to announce a gradual return of US diplomats to the country and the nomination of a new ambassador. Russia calls its actions in Ukraine a "special operation."
The cabinet secretaries also pledged new assistance worth $713 million for Zelensky's government and countries in the region, where Russia's invasion has raised fears of further aggression by Moscow. Zelensky thanked the US for their "unprecedented assistance of the United States to Ukraine," CNN reported. The report also stated that Blinken and Austen had to take a train from Poland to reach the Ukrainian capital.
Russia intends to discuss issues related to the Ukrainian port city of Mariupol and its Azovstal plant in talks with United Nations Secretary-General Antonio Guterres who will visit Moscow this week, RIA cited the foreign ministry as saying on Monday.
Guterres will meet Russian President Vladimir Putin and then head to Ukraine for talks with President Volodymyr Zelensky, the UN said on Saturday.
The US State Department on Monday said it supported the approval of a possible sale of $165 million worth of ammunition to Ukraine to help the country defend itself against Russia's ongoing invasion.
The Ukrainian government had asked to buy various rounds of so-called non-standard ammunition, the department said in a statement, referring to ammunition that does not adhere to NATO standards.
Casualties
One person was killed and another seven were injured in shelling in Poltava Oblast by Russian forces, the governor Dmytro Lunin said on Telegram. He added that buildings were damaged and that the shelling at the thermal power station has left many districts with power outages and no hot water. These statements were echoed on Telegram by Serhiy Hayday, head of the Luhansk regional military administration.
215 children have been killed since the Russian invasion started, according to an update by Ukrainian Ombudsman Lyudmyla Denisova, saying that another two children were killed on Sunday. The ombudsman also stated that Russian forces had set up a concentration camp in the Kharkiv Oblast, where they are allegedly torturing civilians and are "forcing them to cooperate."
Russian casualties as of Monday include nearly 22,000 personnel, 884 tanks, 181 aircraft, 411 artillery systems, 2,258 armored personnel vehicles, 154 helicopters, 76 fuel tanks and eight boats, according to an update by the Ukrainian General Staff of Armed Forces. An intelligence update by the Ukrainian Defense Ministry alleged that Russia's Defense Ministry is hiding their real casualty numbers from their domestic population, citing that the ministry proposing compensation payments to families of deceased service personnel to be overseen by military officials rather than civilians as proof.
Russian forces have killed 3,818 Ukrainians and injured another 4,000 since the invasion began, according to the Ukrainian prosecutor's office, but Ukrainian Prosecutor-General Iryna Venediktova told Interfax in an exclusive interview that these numbers, along with statistics provided by the UN, may be incorrect.
About 33 thousand people evacuated Ukraine on Sunday, according to the Ukrainian State Border Guard Service.