Ukraine leader says Biden should have met him before Putin summit
"It would be better to have this meeting before the summit of the two presidents," Zelensky said in an interview with international news agencies including AFP.
Zelensky is seeking Washington's support for Ukraine's years-long conflict with Russian-backed separatists.
On Friday, the Pentagon announced a new $150 million (1.2-million-euro) package of military assistance for Kiev.
After a lull last year, fighting escalated at the start of 2021 and in April Russia amassed 100,000 troops near the Ukrainian border and in Crimea, prompting warnings from NATO.
The conflict in eastern Ukraine -- including an escalation of tensions since the start of 2021 -- is expected to be high on the agenda in Geneva.
Zelensky on Monday reiterated his country's readiness to join NATO.
"We are fighting a war. This is proof we are ready to join (NATO). We are proving every day that we are ready to be in the alliance more than most of the EU countries," Zelensky said in the interview.
Ukraine, which applied to join the US-led alliance in 2008, is pressing Western powers for more support as it seeks to deter any new aggression from Moscow.
But NATO members remain reluctant to embrace Ukraine as they want to avoid ratcheting up tensions with Russia.
Kiev has been battling pro-Russia separatists in the eastern Donetsk and Lugansk regions since 2014, following Moscow's annexation of the Crimean peninsula. The war has claimed more than 13,000 lives.
Kiev and its Western allies accuse Russia of sending troops and arms to support the separatists, which Moscow has denied.