Russian representatives were not present at the weekend talks, which opened in Florida.
They were originally expected to attend the negotiations, which were due to take place in Abu Dhabi.
The US team is led by special envoy Steve Witkoff and Jared Kushner, President Donald Trump's son-in-law.
Zelenskiy on Sunday called for tougher action against Russia's so-called shadow fleet and for Moscow to be denied oil revenue.
"Revenues give Russia a sense of impunity and the ability to continue the war. That is why pressure must continue and sanctions must work," Zelenskiy said on X.
"Russia's shadow fleet must not feel safe in European waters or anywhere else. Tankers that serve the war budget can and must be stopped and blocked, not just let go."
The French Navy seized an oil tanker in the Western Mediterranean last week that President Emmanuel Macron said was part of Russia's shadow fleet, a network of vessels used to export oil despite Western sanctions.
The shadow fleet, which has grown following Western sanctions on Russia aimed at curbing Moscow's oil revenues, has helped to keep Russian oil exports flowing.
Elements of the peace plan being promoted by the US include a presidential election in Ukraine, alongside territorial concessions.
Zelenskiy, whose term has already expired, is under renewed pressure from Trump to hold a vote as Washington pushes Kyiv towards a peace deal.
Ukrainian law bars wartime elections, but Zelenskiy has said Ukraine would be ready to hold democratic elections if the US secured a two-month ceasefire to allow time to prepare infrastructure and put security guarantees in place.
But Ukraine's former top general, Valeriy Zaluzhnyi, now ambassador to Britain and seen as a potential presidential candidate, said Ukraine needed not elections, but peace won through war.
"What Ukraine needs is not time to prepare for and hold elections, but a peace won through war, which will secure a future for our children," he wrote in an article published on Sunday by Ukrainian outlet NV.
