With the war now in its fourth year after Russia's February 2022 invasion of its neighbour, the effort is draining resources on both sides, although Russia has more resources and people to sustain its fight.
Ukraine is seeking further support from Western partners.
"They are not advancing. It's very tough for our guys out there. And it's tough everywhere," Zelenskiy told reporters.
"It's also very hard for the Russians — and that's good for us."
Russia has claimed the capture of some villages and hamlets in recent weeks, but no defensively stronger urban areas have fallen to its troops.
Russian sabotage and reconnaissance groups have repeatedly attempted to stage minor incursions near Pokrovsk in the eastern Donetsk region to film symbolic footage, such as raising a Russian flag, but Ukrainian forces have repelled those efforts, Zelenskiy said.
Zelenskiy described the situation in the northeastern Sumy border region as "much better" than in recent months, noting progress by Ukrainian forces over the past six weeks.
Russia has also intensified its bombardment of Ukrainian cities, with the second-largest city Kharkiv, struck with a powerful glide bomb for a second straight day on Friday.
Seven people were injured, officials said. On Thursday, 42 were injured.
Joyce Msuya, the United Nations' deputy humanitarian chief, told the Security Council on Friday that Ukraine's humanitarian situation is deteriorating due to expanding Russian attacks on civilian areas across the country.
"There is no safe place left in Ukraine," she said.
Zelenskiy said Ukraine is working with international partners to secure 10 US-made Patriot air defence systems, which can shoot down missiles, with three already confirmed from Germany and Norway.
The Trump administration will sell the systems, he said, but Ukraine's task is to find funding for all 10.
Each system costs more than $US1 billion ($A1.5 billion).
Ukraine is also seeking to obtain a licence to manufacture the Patriot systems itself.
The Ukrainian leader expressed little hope for progress in direct talks between delegations from Russia and Ukraine, though he said the Kremlin envoys have begun discussing the possibility of a leaders' summit with Ukraine.
"We need an end to the war, which probably begins with a meeting of leaders. It won't work any other way with (the Russians)," Zelenskiy said.
The Kremlin, however, remained set against top-level talks before a potential comprehensive peace agreement is fleshed out.
"A high-level meeting can and must put a final point in the settlement and seal the modalities and agreements that are yet to be worked out by experts," Kremlin spokesman Dmitry Peskov said Friday.
"It's impossible to act otherwise."
In domestic politics, Zelenskiy said public protests against changes earlier this week to Ukraine's anti-corruption law were "legitimate".
The changes threatened the independence of anti-graft watchdogs and also drew rebukes from European Union officials and international rights groups, prompting Zelenskiy to propose new legislation to restore the independence of the anti-graft agencies.
"It's very important that society speaks. I respect the opinion of society," Zelenskiy said.
"People asked for changes. We responded."
Demonstrators gathered for the third day on Thursday evening, but drew a smaller crowd.
He said those agencies must be "truly independent," adding that "the most important thing in this war is the unity of our state. It is critical not to lose unity".
However, the risk now remains that the Verkhovna Rada, Ukraine's parliament, will fail to approve the new bill, which could bring even larger crowds to the streets.
Zelenskiy expressed confidence that it would pass in a vote scheduled for July 31.
