Mr Zelensky said some of the aid had started to arrive, but added that it needed to be delivered faster.
He was speaking alongside Nato chief Jens Stoltenberg, who said "it's not too late for Ukraine to prevail".
The comments come after Russia said it had taken a second village in two days in the course of its offensive in eastern Ukraine.
At a joint press conference in Kyiv, President Zelensky said: "The Russian army is now trying to take advantage of a situation when we are waiting for supplies from our partners, especially from the United States of America.
"And that is exactly why the speed of deliveries means stabilising the front."
He specifically singled out Ukraine's need for artillery shells and air defence systems.
"Our partners have all of these things and they should be working now here in Ukraine destroying the Russian terrorist ambitions.
"Russia's army is preparing for further offensive actions," said Mr Zelensky.
Mr Stoltenberg agreed that Kyiv needed weapons, saying that "Ukraine has been outgunned for months, forced to ration its ammunition".
The Nato chief said the six-month delay in US military aid had resulted in "serious consequences on the battlefield".
But Mr Stoltenberg added that he was optimistic that when the arms were delivered it would help turn the tide.
"Our allies are looking into what more they can do and I expect new announcements soon. So we are working hard to meet Ukraine's urgent needs," said the Nato chief.
Russia said it had captured the village of Semenivka, which lies north of Avdiivka which Moscow took in February. On Sunday, Russia said the nearby village of Novobakhmutivka had fallen to its forces.
Ukraine's commander-in-chief Oleksandr Syrskyi has said the situation on the frontline has worsened in the face of multiple Russian attacks, and that Ukrainian forces had withdrawn from positions in the eastern Donetsk region.
Earlier this month, the US finally approved billions of dollars in new military aid for Ukraine to help combat Russia's invasion, putting an end to six months of congressional deadlock and raising Kyiv's hopes that its dwindling supplies would be restocked.
Ukrainian forces have suffered from a shortage of ammunition and air defence systems in recent months. Officials have blamed delays in military aid from the US and other Western allies for the loss of lives and territory.
