The two First Ladies met at a school in Uzhhorod, a town located at the Slovakia-Ukraine border.
The sprawling seaside steel mill where an estimated 2,000 Ukrainian fighters were making a last stand is the only part of the city not under Russian control.
Prime Minister Narendra Modi on Tuesday again appealed to Russia and Ukraine to have an immediate ceasefire and to take path of dialogue as his Danish counterpart Mette Frederiksen hoped that India will influence Russia to stop the crisis.
He said that the evacuees are set to arrive in southern Ukraine's city of Zaporizhzhia on Monday, Xinhua news agency reported.
Ukrainian President Volodymyr Zelensky announced that another mass grave has been discovered in the Kiev region with 900 bodies.
Canada closed its embassy in Kiev on February 12 and relocated diplomatic staff to the western city of Lviv.
After his arrival in Ukraine, Guterres also visited Borodyanka, a town north-west of Kiev destroyed due to Russian shelling.
The Nato chief said Ukraine's allies are preparing to provide it with NATO-standard weapons.
Russia's starting position is that atomic war should be unacceptable and Moscow successfully persuaded the US and other nuclear powers to agree on that back in January, Russian Foreign Minister Sergey Lavrov outlined in an interview.
The UN chief expressed his support for Turkey's ongoing diplomatic efforts in relation to the conflict in Ukraine, Farhan Haq, Guterres' Deputy spokesman, told reporters in New York.
The Prime Minister also confirmed that the UK will reopen its embassy in Kive next week, a move first announced on Friday.
In his latest video address, Zelensky said: "Unfortunately, Russia rejected the proposal to establish an Easter truce.
Shoigu said that the Russian forces had announced ceasefires and opened humanitarian corridors for two hours a day for the past two days on Putin's orders to allow those inside the Azovstal plant to leave.
Israel, he said, would consider it "a great honour" to host possible talks between the Russian and Ukrainian heads of state.
Mariupol, a key Azov Sea port city in eastern Ukraine, saw one of the worst violence in the Russia-Ukraine conflict.
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