Zelensky said that the fight against Russia will continue to be "bloody," but that diplomacy would be the only way to end the conflict decisively.
The Ukrainian president demanded a Russian withdrawal to pre-invasion positions as a pre-condition for any negotiations.
"Its goals are absolutely clear and noble," Putin said about the continued military invasion of Ukraine.
"This is genocide—the elimination of the whole nation and the people," Ukraine's president said.
The Ukrainian negotiator foresees a meeting of the presidents and the initialing of an agreement if it is approved.
A new round of face-to-face diplomatic talks is set to take place sometime this week between Ukraine and Russia.
Four rounds of peace talks have failed to reach a resolution, with significant disagreement over Russia's many demands of Ukraine.
On Monday, Ukrainian presidential adviser Mykhailo Podolyak said that a "technical pause" was placed on negotiations with Russia.
Houthi rebels have pushed forward in a siege to capture Yemen's last remaining government-controlled territory in Marib, an oil-rich northern province.
Three rockets were fired at the presidential palace in a suspected Taliban attack, though no injuries were reported.
Mohammad Javad Zarif, the Iranian Foreign Minister, urged delegates to "take difficult decisions today for the future of their country."
Zhang Jun, China's permanent representative to the U.N., said Sunday that Beijing is "very much concerned about the alarming, worrisome situation in the occupied territory of Palestine."
In the days leading up to a United Nations-led summit on Afghanistan's peace process, a former adviser to the Afghan government said he does not expect the cooperation of the Taliban.
United States Secretary of State Mike Pompeo said the military is on track to completely withdraw all troops from Afghanistan by spring 2021.
Book 16 and 17 of the series are both due out in 2020.
Even if the current "reduction of violence" holds, there is no guarantee that full talks between the Taliban and the government will succeed.
The week-long "reduction in violence" could—if successful—be a prelude to the end of the 18-year conflict.
"We have consistently stressed that genuine peace is possible when the Taliban stop the killing of Afghans, embrace an inclusive ceasefire, and enter into direct negotiations with the Afghan government," Afghan government spokesman Sediq Sediqqi wrote Sunday.
Afghanistan will likely never become an American-style democracy. But the U.S. must ensure its peace agreement with the Taliban allows no return to the status quo ante.
While not uncommon, the request comes at a moment of high tension in Washington as Democrats grow increasingly frustrated by what they view as the Trump administration's obstruction of their oversight responsibilities.
President Moon Jae-in now has two Pungsan pooches to look after.
"North Korea does have diligent people and rich resources," Abe said.
Allies of the president's son-in-law, Jared Kushner, apparently don't think this spells an end to the peace process.
The U.S. has said it will not attend Moscow-led peace talks scheduled for Friday.
With the United States now taking a diplomatic back seat, Russia - whose military intervention turned the tide of Syria's war and helped President Bashar al-Assad recapture Aleppo - is potentially a kingmaker.