United Nations Secretary-General Antonio Guterres told an emergency session of the 193-member General Assembly on Ukraine on Monday that the idea of a nuclear conflict was "simply inconceivable."
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Russian President Vladimir Putin put Russia's nuclear deterrent on high alert on Sunday, a development Guterres described as a "chilling development."
Guterres said told the assembly he hoped those discussions could lead to a halt in the fighting.
"The guns are talking now, but the path of dialogue must always remain open," he said. "We need peace now."
Assembly President Abdulla Shahid asked envoys from member nations to stand for a moment of silence at the start of the session, the assembly's first emergency meeting in decades. Shahid repeated calls for an immediate cease-fire, maximum restraint by all parties and "a full return to diplomacy and dialogue."
Ukraine and its allies on Monday called for a United Nations inquiry into possible war crimes committed by Russia during its military actions in Ukraine.
The United Nations Human Rights Council voted on Monday to accept Ukraine's request to hold an urgent debate on Thursday on Russia's invasion. A Ukrainian draft resolution will be considered at the urgent debate.
If adopted, a commission of three independent experts would investigate all alleged violations of international law in Crimea and the Donetsk and Luhansk regions since 2014 and in other areas of Ukraine since Russia's invasion last week.
Ukraine's ambassador to the United Nations in Geneva, Yevheniia Filipenko, told the Human Rights Council: "Russian forces attempt to sow panic among the population by specifically targeting kindergartens and orphanages, hospitals and mobile medical aid brigades thus committing acts that may amount to war crimes."
Sheba Crocker, U.S. ambassador to the U.N. in Geneva, said in a statement to Reuters that Monday's vote to hold the debate showed Russia was totally isolated on the Council.
"Only 4 countries supported Russia's position, clearly demonstrating the international community is united in condemning Russia's egregious action," she said.
The move by the UNHRC came after least 11 people were killed on Monday in rocket strikes by Russian forces on residential districts of the Ukrainian city of Kharkiv, according to head of the regional administration, Oleg Synegubov.
The northeastern city, Ukraine's second largest, has become one of the major battlegrounds since Russia invaded Ukraine last week in the biggest assault on a European state since World War II.
Synegubov said Russian forces were firing artillery at residential areas of Kharkiv where there are no Ukrainian army positions or strategic infrastructure.
"This is happening in the daytime, when people have gone out to the pharmacy, for groceries, or for drinking water. It's a crime," he said.
Eleven people were killed on Monday and dozens wounded, he said.
It was not immediately possible to independently verify the casualty figures. Earlier Interior Ministry adviser Anton Herashchenko said Russian rocket strikes on Kharkiv on Monday had killed dozens of people.
Russia calls its actions in Ukraine a "special operation" that it says is not designed to occupy territory but to destroy its southern neighbour's military capabilities and capture what it regards as dangerous nationalists.
On Sunday, Ukraine's health ministry said 352 civilians, including 14 children, had been killed since the beginning of the invasion.
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