“Do not be afraid to take the path out of this war. That is the main thing that is required of you now,” he implored.
He said Ukraine was proposing to end the war “through direct engagement between us”.
Zelensky said face-to-face negotiations could take place in a country such as Switzerland or Turkey.
Ukrainian Foreign Minister Andriy Sybiha said “this open letter is a serious and meaningful proposal to end the war”.
“We expect a meaningful response to this proposal. It’s time to end this war. It’s time to choose peace,” he added.
The Ukrainian president’s letter came on the same day Putin was in St Petersburg, where a major economic forum is taking place.
The previous day Kyiv had launched a drone attack on the city’s outskirts, a strike mentioned in Zelensky’s message as “paying a visit”.
Separately Russian-backed authorities in occupied Crimea blamed Ukraine for the death of four people in attacks on the regional capital, Simferopol. Ukraine said it had hit a fuel depot.