Ukrainian President Volodymyr Zelenskiy said Russia was taking advantage of slow deliveries of Western weapons in its offensive.
Zelenskiy said some aid is starting to arrive, but added that it needs to arrive sooner.
Speaking alongside NATO chief Jens Stoltenberg, he said: “It's not too late for Ukraine to win.”
The comments came after authorities at the Black Sea port of Odesa announced that four people had been killed and 32 injured in a Russian missile attack.
Odesa regional director Ole Kiper said three women and one man were killed, and the injured included a 4-year-old, a 16-year-old and a pregnant woman. Private residences and infrastructure were reportedly damaged.
Russia announced early Monday that it had captured its second village in two days during an offensive in eastern Ukraine.
“The Russian military is currently trying to take advantage of the situation where it is waiting for supplies from its partners, especially from the United States,” President Zelenskiy said at a joint press conference in Kiev.
“That’s why speed of delivery means stability on the front.”
He specifically pointed out that Ukraine needs artillery shells and air defense systems.
“Our partners have all of this, and they should be working right now to crush Russia's terrorist ambitions here in Ukraine.
“Russian forces are preparing for further offensive actions,” Zelenskiy said.
Stoltenberg agreed that Kiev needed weapons, saying: “Ukraine has been outgunned for months and has been forced to ration ammunition.”
The NATO chief said the six-month delay in US military aid had “serious consequences on the battlefield”.
But Stoltenberg added that he was optimistic that the delivery of weapons would help turn the tide.
“Our allies are considering what more they can do and we expect further announcements soon. That's why we are working hard to respond to Ukraine's urgent needs,” NATO said. the chief said.
Stoltenberg also stressed that Ukraine would one day become a NATO member, an important strategic goal for Kyiv. But he added that it was unlikely he would be formally invited to the alliance's Washington summit in July.
Russia announced it had captured the village of Seminivka, north of Avdiivka, which Moscow captured in February. Russia announced on Sunday that the nearby village of Novakmutivka had fallen into Russian military hands.
Ukrainian commander-in-chief Oleksandr Shirushkyi said that the situation on the front has deteriorated in the face of repeated Russian attacks, and that Ukrainian forces have withdrawn from their positions in eastern Donetsk.
Also on Monday, Ukraine's Interior Ministry said a 98-year-old woman walked more than 10 kilometers (10 kilometers) with two sticks while coming under shelling from the partially occupied Russian village of Ocheretine in eastern Russia to the Kiev-controlled region. .
“I survived that war. [World War Two], and I am experiencing this war,'' a woman, identified only as Lidiya Stepanivna, can be heard saying in the video at the relief center. She fell several times during her escape and had to rest on the ground, she said.
“This war is different from that war,” she added. “Houses are on fire and trees are uprooted.”
Earlier this month, the United States finally approved billions of dollars in new military aid to Ukraine to counter Russian aggression, ending six months of congressional gridlock and replenishing dwindling supplies. Kiev's expectations were high that this would be the case.
Ukraine's military has suffered from shortages of ammunition and air defense systems in recent months. Officials blame delays in military aid from the United States and other Western allies for the loss of life and territory.