According to five people briefed on the talks, Russia and Ukraine have made significant progress on a peace plan that includes a ceasefire and withdrawal of Russian troops.
Two people said that the proposed deal was discussed in full for the first time on Monday. The people said that the draft would involve Kyiv giving up its ambitions to join Nato and agreeing not to host foreign military bases or weaponry in exchange for protection from allies such as the US, UK and Turkey.
The nature of western guarantees for Ukrainian security and the status of the country's territories seized by Russia could prove to be obstacles to a deal. The 1994 agreement underpinning Ukrainian security did not stop the aggression against it by the Kremlin.
Although Moscow and Kyiv both said they had made progress on the terms of a deal, Ukrainian officials are skeptical that Moscow could be buying time to regroup its forces and resume its offensive.
There is a chance that this is a trick and an illusion. A Ukrainian source briefed on the talks said that they lie about everything.
We need to put pressure on them until they agree to a peace deal, the person said.
Putin vowed that Moscow would achieve all of its aims in Ukraine.
A Russian source briefed on the talks said the proposed settlement could give both sides a way to declare victory in the war.
The person said that every side needs a win. Putin can say that we wanted to stop Ukraine from joining Nato. He can say that if they do that.
Three people familiar with the matter said that Israel's Prime Minister Naftali Bennett has been the primary international mediator on the talks, following a surprise visit to Moscow on March 5.
The president of Turkey spoke with the leader of Ukraine as he and his top officials intensified their efforts to broker a peace deal between the two countries.
Mykhailo Podolyak, a senior adviser to Zelensky, told the Financial Times that any deal would involve the troops of the Russian Federation leaving the territory of Ukraine.
Ukraine would not be allowed to host foreign military bases on its territory and would have to stay out of military alliances such as Nato.
Putin's press secretary told reporters on Wednesday that there was a possibility of neutrality for Ukraine based on the status of Austria or Sweden.
The option is being discussed and can be considered neutral.
The exact wordings of the negotiations were close to being agreed, according to Sergei Lavrov, Russia's foreign minister.
On Wednesday, Ned Price, the US state department spokesman, told reporters that Washington welcomed the expressions of hope and optimism about the diplomatic talks between Russian and Ukraine. There was no indication that Putin was changing his course.
Despite the progress in peace talks, Ukraine's cities came under heavy shelling for a third night in a row.
Russian troops bombed and destroyed a theatre in Mariupol, where hundreds of people had taken shelter, according to local officials.
Zelensky and his aides have played down the country's chances of joining the military alliance, which Russia sees as a provocation.
There is no effective system of European security. As soon as a war began in Europe, Nato stepped aside.
We propose a Ukrainian model of security guarantees, which would include immediate and legally verified participation of a number of guarantor countries in the conflict on the side of Ukraine.
Ukraine would retain its own army as part of any deal. He played down the significance of a ban on foreign bases in Ukraine, saying that it was already barred by Ukrainian law.
There are provisions in the deal for the Russian language to be enshrined in Ukrainian, where it is the only official language. Russia has claimed that its invasion is an attempt to protect Russian speakers in Ukraine from neo-Nazis.
Russia wants Ukraine to recognise its annexation of Crimea and the independence of two statelets in the east of the country.
Podolyak said that Ukraine was willing to compartmentalise the issue.
US president Joe Biden approved a package of new military aid for Ukraine, including anti-aircraft weapons and drones, in order to bolster the country's defences against Russia.
Zelensky made a gut-wrenching appeal for members of Congress and Biden to help his country as it fights back against Russia.
While Biden has refused to entertain US troops on the ground, or enforce a no-fly zone over Ukraine, he signed an 800 million dollar security aid package on Wednesday.
He said that they would give the army to fight and defend themselves through the difficult days ahead.
The new package includes drones, which the president said showed America's commitment to send in our most cutting-edge systems to Ukraine for its defence.
Additional reporting by Laura Pitel in Ankara.