Russian forces intensified shelling of cities in Ukraine's centre, north and south, a Ukrainian official said, as a second attempt to evacuate besieged civilians collapsed.

With the Ukrainian leader urging his people to take to the streets to fight, Russian President Vladimir Putin shifted blame for the invasion, saying Moscow's attacks could be halted “only if Kyiv ceases hostilities.”

The outskirts of Kyiv, Chernihiv in the north, Mykolaiv in the south, and Kharkiv, the country's second-largest city, faced stepped-up shelling late Sunday, presidential adviser Oleksiy Arestovich said. Heavy artillery hit residential areas in Kharkiv and shelling damaged a television tower, according to local officials.

The attacks dashed hopes that more people could escape the fighting in Ukraine, where Russia's plan to quickly overrun the country has been stymied by fierce resistance.

Russia has made significant advances in southern Ukraine and along the coast, but many of its efforts have become stalled, including an immense military convoy that has been almost motionless for days north of Kyiv.

Food, water, medicine and almost all other supplies were in desperately short supply in the southern port city of Mariupol, where Russian and Ukrainian forces had agreed to an 11-hour cease-fire that would allow civilians and the wounded to be evacuated. But Russian attacks quickly closed the humanitarian corridor, Ukrainian officials said.

“There can be no green corridors' because only the sick brain of the Russians decides when to start shooting and at whom,“ Interior Ministry adviser Anton Gerashchenko said on Telegram.

A third round of talks between Russian and Ukrainian leaders is planned for Monday.

Ukrainian President Volodymyr Zelenskyy rallied his people to remain defiant, especially those in cities occupied by Russians.

“You should take to the streets! You should fight!” he said Saturday on Ukrainian television. “It is necessary to go out and drive this evil out of our cities, from our land.”

Zelenskyy also asked the United States and NATO countries to send more warplanes to Ukraine, though that idea is complicated by logistical questions about how to provide aircraft to Ukrainian pilots.

He later urged the West to tighten its sanctions on Russia, saying that “the audacity of the aggressor is a clear signal" that existing sanctions are not enough.

The war, now in its 12th day, has caused 1.5 million people to flee the country. The head of the UN refugee agency called the exodus “the fastest-growing refugee crisis in Europe since World War II."

A senior US defense official said Sunday that the US assesses that about 95 per cent of the Russian forces that had been arrayed around Ukraine are now inside the country.

The official said Russian forces continue to advance in an attempt to isolate Kyiv, Kharkhiv and Chernihiv, but are being met with strong Ukrainian resistance.

The official, who spoke on condition of anonymity to discuss military assessments, said the convoy outside Kyiv continues to be stalled.

As he has often done, Putin blamed Ukraine for the war, telling Turkish President Recep Tayyip Erdogan on Sunday that Kyiv needed to stop all hostilities and fulfil “the well-known demands of Russia."

Putin launched his invasion with a string of false accusations against Kyiv, including that it is led by neo-Nazis intent on undermining Russia with the development of nuclear weapons.

The Russian Defence Ministry on Sunday announced that its forces intend to strike Ukraine's military-industrial complex with what it said were precision weapons.

A ministry spokesman, Igor Konashenkov, claimed in a statement carried by the state news agency Tass that Ukrainian personnel were being forced to repair damaged military equipment so that it could be sent back into action.

Zelenskyy criticized Western leaders for not responding to Russia's latest threat.

“I didn't hear even a single world leader react to this,” Zelenskyy said Sunday evening.

The Russian Defence Ministry also alleged, without providing evidence, that Ukrainian forces are plotting to blow up an experimental nuclear reactor in Kharkiv and to blame it on a Russian missile strike.

Putin and French President Emmanuel Macron spoke Sunday about the nuclear situation in Ukraine, which has 15 nuclear reactors at four power plants and was the scene of the 1986 Chernobyl nuclear disaster.

The men agreed in principle to a “dialogue” involving Russia, Ukraine and the UN's atomic watchdog, according to a French official who spoke on condition of anonymity, in line with the presidency's practices. Potential talks on the issue are to be organized in the coming days, he said.

Putin also blamed the fire last week at the Zaporizhzhia nuclear plant, which Ukrainian officials said was caused by Russian attackers, on a “provocation organized by Ukrainian radicals."

International leaders, as well as Pope Francis, appealed to Putin to negotiate.

In a highly unusual move, the pope said he had dispatched two cardinals to Ukraine to try to end the conflict.

“In Ukraine, rivers of blood and tears are flowing,” the pontiff said in his traditional Sunday blessing.

The death toll remains unclear. The UN says it has confirmed just a few hundred civilian deaths but also warned that the number is a vast undercount.