Since taking office in January, US President Donald Trump has paused US military aid to Ukraine as well as intelligence-sharing.
He has accused Zelenskiy of not being serious about reaching a peace agreement with Russia, which invaded Ukraine three years ago and has seized about 20 per cent of its territory.
"Ukraine has been seeking peace from the very first second of this war. Realistic proposals are on the table. The key is to move quickly and effectively," Zelenskiy said on social media network X.
Zelenskiy said he would visit Saudi Arabia next week and that after meeting with Crown Prince Mohammed Bin Salman on Monday, Ukrainian diplomatic and military representatives would stay for a meeting on Tuesday with the US team.
"On our side, we are fully committed to constructive dialogue, and we hope to discuss and agree on the necessary decisions and steps," he said.
The Ukrainian delegation will include Foreign Minister Andrii Sybiha, Zelenskiy's chief of staff Andriy Yermak and Defence Minister Rustem Umerov.
Trump's special envoy Steve Witkoff has also said he was in discussions with Ukraine for a framework deal to end the three-year war with Russia, and a meeting was planned next week with a Ukrainian delegation in Saudi Arabia.
In February, Saudi Arabia hosted a meeting between US and Russian officials to discuss ways to halt the deadliest conflict in Europe since World War II.
Ukraine was not included in those talks, raising concern among officials in Kyiv and among its European allies.
Zelenskiy met Trump at the White House on February 28 but the encounter descended into acrimony when they clashed in front of the world's media over peace moves.
Meanwhile, war bloggers and a senior Russian commander said on Saturday that Russian troops had launched a large-scale offensive to retake swaths of the western Kursk region from Ukrainian forces.
Ukrainian troops invaded Russia's Kursk region last summer, taking chunks of territory in an unexpected lightning attack more than two years after Russian President Vladimir Putin ordered tens of thousands of troops into Ukraine.
"In all directions of the Kursk section of the front, all units have launched a large-scale offensive," Major General Apti Alaudinov, commander of a Chechen unit fighting for Russia in Kursk, said on Telegram.
"The enemy is abandoning its positions."
Reuters was unable to verify the situation on the battlefield.
Ukraine's military did not immediately comment.
Open source maps showed this week that Ukraine's positions in Kursk have deteriorated sharply and its troops are nearly surrounded by Russian forces.
Pro-Russian war blogger Two Majors said on Saturday Russian troops had begun an assault on Sudzha, a town 9.5km from the border with Ukraine, and that the situation for Ukrainian troops there was "close to critical".
Major General Alaudinov said Russian airborne brigades, motorised rifle regiments and the Akhmat special forces were taking part in "fierce battles" and "our guys are moving forward very well".
Russian troops recaptured three villages in Kursk - Viktorovka, Nikolaevka and Staraya Sorochina - from Ukraine on Saturday, the defence ministry said.
Reuters could not independently verify its report.
