Ukrainian President Volodymyr Zelenskyy reflected on his meeting with the United Nations Security Council in his daily speech Tuesday.

Zelenskyy said the council is "currently unable to carry out the functions for which it was created."

"The U.N. Security Council exists, and security in the world doesn’t, for anyone," he said. "And only one state is to blame for this, Russia, which discredits the U.N. and all other international institutions where it still participates."

Zelenskyy added that Russia "tries to block everything constructive and use global architecture in order to spread lies and justify the evil it does."

"I'm sure the world sees it. I hope the world will draw conclusions," he said.

-ABC News' Christine Theodorou

Nearly 1,500 people were evacuated from the heavily bombed southeastern Ukrainian city of Mariupol in private cars on Tuesday, Ukrainian officials said.

The evacuees left Mariupol in private vehicles because evacuation buses and humanitarian cargo could not make it into the city, officials said.

Ukrainian Deputy Prime Minister Iryna Vereshchuk said that in addition to the evacuees in Mariupol, another 3,846 people evacuated from other towns across the country, including 1,080 from the Luhansk separatist area of eastern Ukraine.

The evacuation came as Igor Konashenkov, a spokesperson for the Russian Ministry of Defense, said on Tuesday that Mariupol would be "liberated from nationalists" by Russian forces, according to the Russian state-run TASS news service.

Konashenkov also said Moscow has repeatedly offered Ukrainian troops in Kyiv a chance to lay down their arms and that the offer was extended again on Tuesday morning.

"However, these proposals are constantly ignored by the Kyiv regime," Konashenkov said, according to TASS.

France on Tuesday offered to send a forensics team to Ukraine to collect evidence for an investigation of alleged war crimes committed by Russian forces.

French President Emmanuel Macron made the offer during a phone conversation Tuesday with Ukrainian President Volodymyr Zelenskyy, according to a readout made public by the Elysee Palace, the French leader's official residence. Macron also offered to contribute $534,000 to the International Criminal Court in The Hague to assist in its investigation into war crimes committed in Ukraine.

Macron also offered to dispatch French personnel, including two magistrates and 10 police officers, to help in the investigation.

During the call, Macron conveyed to Zelenskyy the "shock and emotion" caused in France by images of dead civilians in the streets of Bucha, near the capital of Kyiv.

-ABC News' Christine Theodorou

At least 12 people were killed, including a child, in an attack on Monday by Russian troops on the southern Ukraine city of Mykolaiv, the governor of the Mykolaiv region confirmed.

The attack in Mykolaiv near the Black Sea included the shelling of an oncology hospital, said Vitaliy Kim, governor of the Mykolaiv region. The Ukrainian General Prosecutor's office said 41 people were wounded in the attack, including four children.

Four members of Doctors Without Borders/Medecins Sans Frontieres were at the hospital when it came under attack, said Michel-Oliver Lacharite, head of the group's mission in Ukraine.

"Several explosions took place in close proximity to our staff over the course of about 10 minutes," Lacharite said in a statement. “As they were leaving the area, the MSF team saw injured people and at least one dead body. However, we are not in a position to give exact numbers of dead and injured."

-ABC News' Christine Theodorou