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Presidential adviser Mykhaylo Podolyak said concessions would lead to an even larger and bloodier Russian offensive.
His comments come as Russia continues attempts to encircle Ukrainian forces defending Severodonetsk in the east.
In another development, Polish President Andrzej Duda has become the first foreign leader to address the parliament in Kyiv in person.
He received a standing ovation as he declared that only Ukrainians themselves could decide their future.
He added that Poland would do everything it could to help Ukraine join the EU.
However, France's Europe Minister, Clément Beaune, said in a radio interview on Sunday that it would probably take "15 or 20years" for Ukraine to be accepted as an EU member.
As fighting continued, the General Staff of the Ukrainian Armed Forces said in its daily update that Russian forces were trying to break throughUkrainian defences to reach the administrative borders of the country's easternmost Luhansk region.
Luhansk regional governor, Serhiy Haidai, said Russia had attempted to break into Severodonetsk from four separate directions.
Writing on the Telegram messaging app, he said the attempts had been unsuccessful, but shelling of residential areas was continuing.
He added that a bridge connecting the city to nearby Lysychansk had been destroyed.
It was not possible for the BBC to verify the claims independently.
There have been calls in some Western nations for a ceasefire that could involve Russian forces remaining in some of the territory they have occupied inthe south and east of Ukraine since Moscow invaded the country on 24 February.
Most recently, Italian Prime Minister Mario Draghi told his country's Senate on Thursday that a ceasefire "must be achieved as soon as possible".
But Mr Podolyak said that any such moves would backfire.
"The war will not stop. It will just be put on pause for sometime," he said. "They'll start a new offensive, even more bloody and large-scale."
The BBC's Joe Inwood in Kyiv says there is currently no middle ground between what the Russians want and what the Ukrainians would accept.
Our correspondent says that while both sides feel they have a fighting chance, negotiations are unlikely.
Thank you for the article BBC
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