The meeting follows intensified Russian attacks on Ukrainian cities, including Kyiv and Sloviansk, which resulted in casualties and injuries in the days leading up to the talks.
A draft peace proposal, reportedly “about 90 per cent ready”, includes potential security guarantees for Ukraine.
Mr Zelensky has indicated a willingness to drop the country's bid to join Nato in exchange.
Russia's demands for a peace settlement include the recognition of annexed territories, Ukraine's withdrawal from certain eastern areas, and the abandonment of its Nato membership aspirations.