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Representatives from both nations met in Istanbul on Tuesday, marking the first face-to-face meeting between the sides since 10 March.
As a result of negotiations, Russia has agreed to scale down its military operations around the Ukrainian capital of Kyiv and the city of Chernihiv.
In turn, Ukraine put forward fresh proposals regarding adopting a "neutral status".
Speaking at the venue, Mevlut Cavusoglu said Turkey welcomed the two countries reaching compromise and a common understanding on certain issues.
He said "more difficult issues" were expected to be discussed between Ukrainian and Russian foreign ministers at a later date,
Vladimir Medinsky, Russia's chief negotiator, raised the possibility for a face-to-face meeting between Russian president Vladimir Putin and Ukrainian president Volodymyr Zelenskyy.
Tuesday's talks come following reports Russian billionaire Roman Abramovich and two Ukrainian delegates suffered symptoms of a suspected poisoning following previous rounds of peace negotiations.
The Chelsea owner suffered the symptoms after a meeting in Kyiv earlier this month, sources close to the situation said on Monday.
Abramovich and at least two senior Ukrainian peace negotiators were said to have experienced symptoms of suspected poisoning, including red eyes, constant and painful tearing, and peeling skin on their faces and hands.
Here's a look at what was discussed in Tuesday's talks.
Neutral status for Ukraine
Part of the negotiations focused on Russia's requirement for Ukraine to remain neutral, meaning it would have to formally abandon its ambitions to join Nato.
Ukrainian negotiators have proposed adopting a neutral status which would come with international guarantees to protect the country from another attack.
During talks on Tuesday, they proposed a status under which their country would not join alliances or host bases of foreign troops, but would have its security guaranteed in terms similar to "Article 5", the collective defence clause of Nato.
The proposals would include a 15-year consultation period on the status of Russian-annexed Crimea, and could come into force only in the event of a complete ceasefire, the Ukrainian negotiators told reporters in Istanbul.
Ukraine's proposals were the most detailed and concrete that Kyiv has aired publicly.
"If we manage to consolidate these key provisions, and for us this is the most fundamental, then Ukraine will be in a position to actually fix its current status as a non-bloc and non-nuclear state in the form of permanent neutrality," said Ukrainian negotiator Oleksander Chaly.
"We will not host foreign military bases on our territory, as well as deploy military contingents on our territory, and we will not enter into military-political alliances."
Watch: Roman Abramovich seen at Ukraine peace talks in Turkey after poisoning allegations
Russian troops pull back
Russian deputy defence minister Alexander Fomin said Russia had decided to scale down fighting near Kyiv and Chernihiv to create the conditions for dialogue.
As he exited the talks, Fomin told reporters: “The decision has been taken to fundamentally cut back military activity in the direction of Kyiv and Chernihiv."
He made no mention of other areas that have seen heavy fighting, including around Mariupol in the southeast, Sumy and Kharkiv in the east and Kherson and Mykolaiv in the south.
Some analysts noted that Russia's promise to reduce fighting mostly covered areas where it has been losing ground.
Mark Hertling, a retired US lieutenant general and former commander of US forces in Europe tweeted: "Does 'we’ll drastically reduce military operations around Kyiv' = 'we’re getting our a** kicked, transitioned to a hasty defense?'"
Zelenskyy has asked for strict conditions for further progress to be made.
He has demanded Russian troops withdraw to their positions prior to 24 February.
The Ukrainian president has also said any peace deal would need to put to his people in a referendum, arguing his citizens must have a say in any potential territorial changes that would require constitutional revisions.
Russia is now in its second month of the invasion of Ukraine,
While troops have so far failed to take control of any major cities, Moscow's forces have wreaked havoc and devastation on the country.
Towns and cities have been reduced to rubble, and four million Ukrainians have been forced to flee their home country, seeking shelter as refugees.
Cities including Kharkiv and Mariupol have suffered heavy bombardment, and small towns and villages near the capital of Kyiv have born much of the brunt of fighting in recent weeks.
Addressing the Danish parliament on Tuesday, Zelenskyy said some 100,000 people were still trapped in Mariupol, which is encircled by Russian forces and under unceasing bombardment.
Ukrainian authorities have claimed over 17,000 Russian soldiers have died in the offensive, figures which have yet to be independently verified.
An anonymous officer from Nato said on Wednesday that battlefield casualties suffered by Russia are thought to total between 30,000 and 40,000 since Putin launched his invasion on February 24.
British military intelligence said on Thursday that "Russian forces have almost certainly suffered thousands of casualties during their invasion of Ukraine."