Nearly four months after Russia launched a bloody invasion of his country, Zelensky said in his evening address on Sunday there had been "few such fateful decisions for Ukraine" as the one it expects from the European Union this week.
"Obviously, we expect Russia to intensify hostile activity this week ... We are preparing. We are ready," he said.
Leaders of the EU's 27 member states will discuss at a summit on Thursday and Friday whether to add Ukraine to the list of countries vying for membership.
EU foreign ministers gathering in Luxembourg kicked off the week urging Moscow to stop blocking the export of vitally needed grain from Ukraine, a top global supplier.
"One cannot imagine that millions of tonnes of wheat remain blocked in Ukraine while in the rest of the world people are suffering hunger. This is a real war crime," the bloc's top diplomat Josep Borrell said.
Moscow has denied responsibility for the food crisis, and blames Western sanctions for the disrupted deliveries that have pushed up cereal prices and fanned fears of famines in vulnerable regions.
On the ground, Russia appeared to be making some battlefield advances in the east.
In its daily update on Monday, Ukraine's presidency reported heavier Russian shelling in the Kharkiv region in the northeast.
In the Donetsk region, the intensity of the attacks "is growing along the entire frontline" it said, leaving at least one person dead and injuring seven people, including a child.
Fighting also continued in the key industrial city of Severodonetsk in the east, with Ukraine saying it had lost control of the adjacent village of Metyolkine.
"Unfortunately, we do not control Metyolkine anymore. And the enemy continues to build up its reserves," the Lugansk regional governor Sergiy Gaiday said in a statement on social media.
Moscow's forces have for weeks been battling to seize the eastern Donbas region, after being repelled from other parts of the country following their February invasion.
A chemical plant in Severodonetsk where hundreds of civilians are said to be sheltering was being shelled "constantly", Gaiday said.
NATO's chief Jens Stoltenberg meanwhile warned on Sunday that the war could grind on "for years" and urged Western countries to be ready to offer long-term military, political and economic aid.
Ukraine has repeatedly urged Western countries to step up their deliveries of arms, despite warnings from nuclear-armed Russia that it could trigger wider conflict.
Russia's defence ministry said Sunday it launched missile strikes during the past 24 hours, with one attack on a top-level Ukrainian military meeting near the city of Dnipro killing "more than 50 generals and officers".
It said it also targeted a building housing Western-provided weapons in Mykolaiv, destroying Ukrainian artillery and armoured vehicles.
There was no independent verification of the claims.
Mykolaiv is a key target for Russia as it lies on the route to the strategic port of Odessa.
With Russia maintaining a blockade of Odessa that has trapped grain supplies, residents have turned their attention to rallying the home front effort.
"Every day, including the weekend, I come to make camouflage netting for the army," said Natalia Pinchenkova, 49, standing by a large Union flag, a show of thanks to Britain for its support for Ukraine.
The Ukraine war is fuelling not only a global food crisis but an energy crisis too.
Hit by punishing sanctions, Moscow has turned up the pressure on European economies by sharply reducing gas supplies, which has in turn sent energy prices soaring.
Germany on Sunday announced emergency measures including increased use of coal to ensure it meets its energy needs after a drop in the supply of Russian gas in recent days.
Austria announced it will reopen a mothballed coal power station to combat shortages, and Italian company Eni joined a huge Qatari project to expand production from the world's biggest natural gas field.
China's imports of oil from Russia meanwhile jumped by 55 percent year on year in May, customs data showed Monday, as Beijing continued to refuse to condemn Moscow's war.
Natalia Khalaimova, 54, a resident in Lysychansk, across the river from Severodonetsk, said she wanted Russia and Ukraine to negotiate an end to the war.
"Every war in any country ends -- but the sooner, the better," she told AFP. "So many civilians are killed. Most of them were not involved in the war at all."