The statement comes ahead of Monday's planned meeting with Zelenskyj at the White House.
"Ukraine's President Zelenskyj can end the war with Russia almost immediately, if he wants to, or he can continue to fight," writes the American president during the night towards Monday, Swedish time.
He also writes that Ukraine "will not get back Crimea" and that the country "will not join Nato", in capital letters.
Later during the night, Zelenskyj announced that he had arrived in Washington. In a post on the messaging app Telegram, he expresses his desire for an end to the war.
"We all want to quickly and reliably get an end to this war. And the peace must be lasting," he writes in a post on the messaging app Telegram.
Several European leaders, including the President of the European Commission Ursula von der Leyen, will attend Monday's White House meeting.
The peninsula Crimea was illegally annexed by Russia in 2014.
