KYIV (AFP) -- Russian President Vladimir Putin's announcement that his nuclear forces were on alert sparked outcry in the West as the invading troops faced stiff resistance on Monday.

The UN General Assembly will hold a rare emergency session Monday to discuss the conflict, which has claimed dozens of lives and raised fears that it will displace millions of people.

Ukraine has also said it had agreed to send a delegation to meet Russian representatives on the border with Belarus, which would be the two sides' first public contact since war erupted.

Russia invaded on Thursday and quickly announced it had neutralised key Ukrainian military facilities, but fierce fighting has since raged.

Ukraine forces, backed by Western arms, are stymieing the advance of Russian troops, according to the United States, which has led Western condemnation and a campaign of sanctions.

Putin ordered Sunday Russia's nuclear forces onto high alert in response to what he called "unfriendly" steps by the West. Russia has the world's largest arsenal of nuclear weapons and a huge cache of ballistic missiles.

The United States, the world's second largest nuclear power, slammed Putin's order as "totally unacceptable."

Germany said Putin's nuclear order was because his offensive had "halted"

and was not going to plan.

Ahead of the planned talks with Russia and as Ukrainian forces defended key cities, Foreign Minister Dmytro Kuleba voiced defiance.

"We will not capitulate, we will not give up a single inch of our territory," Kuleba said.

Ukrainian President Volodymyr Zelensky said he was sceptical about the talks.

"As always: I do not really believe in the outcome of this meeting, but let them try," he said.

On day four of an invasion that stunned the world, Ukrainian forces said Sunday they had defeated a Russian incursion into Ukraine's second city Kharkiv, 500 kilometres (310 miles) east of Kyiv.

A regional official, Oleg Sinegubov, said Kharkiv had been brought under Ukrainian control and the army was expelling Russian forces.

Moscow has made better progress in the south, however, and said it was besieging the cities of Kherson and Berdyansk.

Both are located close to the Crimean peninsula, which Russia annexed from Ukraine in 2014, and from which it launched one of several invasion forces.

Ukrainian officials said they were fighting off Russian forces in several other areas, and claimed that 4,300 Russian troops had been killed.

In Kyiv, many residents spent another night in shelters or cellars as Ukrainian forces said they were fighting off Russian "sabotage groups."

But Sunday was relatively calm compared to the first days of fighting and the city was under a blanket curfew until Monday morning.

Ukraine has called on its own civilians to fight Russia, with a brewery in Lviv in the country's west switching its production line from beers to bombs, making Molotov cocktails for the volunteer fighters.

Western sources said the intensity of the resistance had apparently caught Moscow by surprise.

Ukraine has reported 198 civilian deaths, including three children, since the invasion began and Russia has acknowledged for the first time that a number of its forces had been killed or injured.

The UN has put the civilian toll at 64 while the EU said more than seven million people could be displaced by the conflict.

"We are witnessing what could become the largest humanitarian crisis on our European continent in many, many years," the EU commissioner for crisis management Janez Lenarcic said.

At the Medyka border crossing with Poland, volunteer Jasinska said the long line of arrivals, mostly women and children, need warm clothes.

Crossing Medyka with his family, Ajmal Rahmani, an Afghan who fled Afghanistan for Ukraine four months before the US withdrawal, told AFP: "I run from one war, come to another country and another war starts. Very bad luck." (AFP)