Ukraine agreed to launch peace talks with Russia on Sunday, even as battles raged in key cities and President Vladimir Putin raised the prospect of a nuclear escalation with the West.
Delegations from each country are set to meet at the Ukrainian-Belarusian border, the office of Ukrainian President Volodymyr Zelensky said.
There are no conditions to the planned talks at the border, according to the statement.
Zelensky had previously refused an offer by the Kremlin to meet in Belarus proper, pointing to the fact that Russia had partially staged its invasion of Ukraine out of that country.
The announcement came as Putin ordered the country's "deterrent weapons" be put on special alert, without specifically mentioning nuclear weapons.
"The top leaders of the leading NATO countries are allowing aggressive statements against our country, so I order the defence minister and the chief of the general staff to put the forces of deterrence of the Russian army on a special regime of alert," Putin said.
NATO Secretary General Jens Stoltenberg has expressed alarm at Putin's decision, saying in a BBC interview on Sunday that the announcement showed how "serious" the situation is.
On the ground, Ukrainian and Russian soldiers were fighting on the streets of Kharkiv in the east, and Ukraine was bolstering its forces to repel advances on the outskirts of the capital Kiev.
Kharkiv citizens were urged to stay in their homes and shelters as local administration chief Oleh Synyehubov said invading forces had managed to break through Ukrainian defences and enter the city centre.
Videos shared on social media showed several military vehicles in the city of about 1.5 million people.
In Kiev, an explosion destroyed seven cars and shattered the windows of a 16-storey apartment, the city authority reported.
It released an image showing a crater that could have been created by a grenade. It could not be independently verified whether Russian forces were behind the attack.
Ukraine has accused Russia of targeting civilians in its invasion of the country - a charge rejected by Moscow.
Kiev mayor Vitali Klitschko wrote on the Telegram messaging app that nine civilians had been killed in the Ukrainian capital in recent days, including a child. Eighteen Ukrainian security forces have also been killed.
According to the mayor, 106 people have been injured so far, including 47 civilians.
Ukraine's deputy foreign minister said troops were being mobilized across the country, with reinforcements focusing mainly on repelling Russian advances north and north-west of the beseiged capital.
The air force have intercepted Russian fighter jets and transport planes over Kiev, and in the south the navy deflected a Russian landing, deputy defence minister Hanna Malyar wrote on Twitter. None of the information could be independently verified.
The general staff of the armed forces of Ukraine claimed that the Russian attack was waning in strength as the invasion entered its fourth day.
"The Russian occupier has reduced the pace of the offensive, but still tries to develop success in some areas in the offensive against Ukraine," a statement posted on Facebook said.
According to the Ukrainian military, Russian troops were struggling to replenish fuel and ammunition.
Malyar said some 4,300 Russian soldiers had died. Russia has not given any details on casualties among its ranks.
Moscow says 471 Ukrainian soldiers have been captured during the fighting in Ukraine.
The violence has already prompted hundreds of thousands of people to flee to neighbouring countries. On Sunday, the UN Refugee Agency put the number of refugees at 368,000 and said it was expected to rise further.
Over 200,000 Ukrainian refugees have arrived in Poland alone, according to the country's border guard.
"More than 28,000 people crossed the border between midnight and 7 this morning [0600 GMT]," a border guard spokeswoman said on Sunday.
At the Medyka-Shehyni border crossing, people on the Ukrainian side reported having to wait up to 30 hours for clearance. The spokeswoman of the Polish border guard said they were working with their Ukrainian colleagues to speed up the procedure.
70,000 refugees in Hungary
In Hungary, around 70,000 people have arrived from Ukraine seeking shelter since the fighting erupted, according to Hungarian police.
By midnight Sunday, over 47,000 Ukrainians had entered Romania, although almost 23,000 had since left the country again, government spokesman Dan Carbunaru said in Bucharest.
The international community has doubled down on its response to the invasion, which was launched in the early hours of Thursday.
A number of European allies are sending arms to Ukraine, including Germany, a major turnaround for Berlin which had staunchly refused to supply lethal weapons to Kiev for weeks in the run up to the Russian invasion.
For its part, Japan also decided to join its partner in the Group of Seven nations by shutting Russia out of the SWIFT international transfer system - a key component of the sanctions packages announced by the United States and the European Union.
Japanese Prime Minister Fumio Kishida also announced on Sunday $100 million dollars in aid for Ukraine, matching similar pledges made by other G7 countries
Many European nations have also banned Russian planes from using their airspace and an EU initiative to extend that measure across the entire 27-member bloc is currently being discussed.
Later Sunday, the United Nations Security Council was due to convene for the fourth time within a week for an emergency meeting to discuss the crisis.
The meeting of the UN's most powerful body will take place at 3 pm (2000 GMT), according to diplomats, who said its purpose was to hold a vote on whether to send a resolution condemning Russia's invasion of Ukraine to the UN General Assembly.
Russia used its veto power to block the resolution at the Security Council on Friday.