The announcement by the Ukrainian president comes a day after US President Donald Trump warned Russia he may send Kyiv long-range Tomahawk missiles
A meeting between Zelenskiy and Trump could take place as early as Friday, the Ukrainian president said, adding that he also would meet with defence and energy companies and members of Congress.
"The main topics will be air defence and our long-range capabilities, to maintain pressure on Russia," Zelenskiy said on Monday.
He spoke at a meeting with EU High Representative for Foreign Affairs Kaja Kallas.
He said he also would seek further US assistance to protect Ukraine's electricity and gas networks, which have faced relentless Russian bombardment.
The US visit follows what Zelenskiy described as a "very productive" phone call with Trump on Sunday.
Trump later warned Russia that he may send Ukraine long-range Tomahawk missiles if Moscow doesn't settle its war there soon. The missiles would allow Ukraine to strike deeper into Russian territory.
Moscow has expressed "extreme concern" over the US potentially providing Tomahawk cruise missiles to Ukraine.
Russian President Vladimir Putin previously suggested that the US supplying long-range missiles to Ukraine would seriously damage relations between Moscow and Washington.
Zelenskiy will join a Ukrainian delegation already in the US for preliminary talks, led by Prime Minister Yulia Svyrydenko.
Russia has stepped up attacks in recent weeks targeting electricity and gas infrastructure ahead of winter, in an effort to cripple Ukraine's power grid ahead of freezing temperatures to erode public morale.
Ukraine's State Emergency Service said the worst attacks early on Monday using drones and missiles occurred around the Black Sea port of Odesa and in the northern Chernihiv region, where one person was killed.
Power outages also occurred in the eastern city of Kharkiv - just 20km from the Russian border - following Russian bombing raids.
Four people were injured in the attacks, Mayor Ihor Terekhov announced on Telegram on Monday.
Kallas, the EU's top diplomat, pledged continued pressure on Moscow.
She also expressed confidence that objections led by Hungary to a new Russia sanctions package would be overcome, even if the process drags on past a meeting of EU leaders next week.
"On funding, the needs are enormous. We must help Ukraine defend itself so we don't later spend even more repairing destroyed infrastructure," Kallas said.
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