Zelenskiy said in an interview aired on Sunday that he wanted to press on with talks on securing peace with Russia, which have stalled in recent months, before the onset of winter to take account of Ukraine's improved strategic position.
Talks brokered by the United States on moving toward a peace accord have ground to a halt as US officials have focused on the conflict in Iran.
Budanov said he expected a US delegation to visit Moscow and Kyiv in the near future, without giving details.
"This is the president's instruction: to try to end this war as soon as possible ... preferably before winter," he told reporters at a press conference.
"In my opinion, this is absolutely correct, timely and realistic."
Zelenskiy and other Ukrainian officials have said the advance of Russian forces has slowed on the ground while Ukraine has intensified a campaign of long-range strikes inside Russia, targeting mainly the oil industry.
A senior Ukrainian commander said last week that Ukraine had a six-month window in which to seize the battlefield initiative and strengthen its hand for peace talks.
Zelenskiy said on Monday that Ukraine's front lines have been "significant strengthening," citing a report from Commander-in-Chief Oleksandr Syrskyi.
Ukraine's top military commander had briefed him on the battlefield situation during a meeting of Ukraine's military leadership, Zelenskiy said.
"Ukrainian positions are strong, and this is a result our state very much needs - one that will certainly support all diplomatic steps," Zelenskiy wrote on Facebook.
The Ukrainian military blog DeepState, which closely tracks developments along the front line using open-source information and tips from army sources, also assessed the situation as largely stabilised.
According to DeepState, Russian forces captured 14 square kilometres of Ukrainian territory in May, the lowest monthly gain in the past three years.
"The war is entering a new stage and it is important for the Ukrainian state not to lose the initiative," the analysts wrote on Telegram.
Russian forces have advanced steadily since the northern hemishpere autumn of 2023, albeit slowly and at heavy cost.
Since the start of the fifth year of the war, however, Ukrainian defenders have managed to stabilise the battlefield situation.
Russia launched its full-scale invasion of Ukraine in February 2022.
with DPA
