Zelenskyy spoke to Trump in the middle of a three-day ceasefire proclaimed by Russian President Vladimir Putin, coinciding with commemorations of the 80th anniversary of the World War 2 victory over Nazi Germany.
Zelenskyy has dismissed the three-day pause as meaningless and each side has accused the other of violating it.
"Ukraine is ready for a complete 30-day ceasefire from this very day, from this very moment," Zelenskyy said in his nightly video address.
"But it has to be real... Thirty days which could become the beginning of years of peace. A ceasefire, both prolonged and reliable, will be a real indicator of a movement towards peace."
The Ukrainian president said Russia had to demonstrate its readiness to end the war, starting with an unconditional ceasefire.
Trump, in a social media post on Thursday (local time), again called for a 30-day unconditional ceasefire, though he made no reference to his conversation with Zelenskyy.
He said that if the 30-day ceasefire "is not respected, the US and its partners will impose further sanctions."
A 30-day ceasefire was initially proposed by Washington in March and Ukraine agreed. Russia has said such a measure can only take effect once reliable measures of monitoring and upholding it are put in place.
Zelenskyy said he also spoke to Trump about the ratification by Ukraine's parliament on Thursday of an agreement to exploit Ukraine's mineral riches along with the creation of an investment fund for Ukraine's reconstruction.
He said he and Trump "noted how important it is that our relationship has strengthened our countries over the decades".
