In his 10-minute address in front of the presidential office in Kyiv, Zelensky warned that Ukraine would face "a lot of pressure... to weaken us, to divide us", adding that "the enemy is not sleeping".
Urging Ukrainians to stay united, he stressed that the country's "national interest must be taken into account".
"We're not making loud statements," he went on, "we'll be calmly working with America and all the partners... offering alternatives" to the proposed peace plan.
Zelensky also said he had been reassured of continuous support during a phone call with UK Prime Minister Sir Keir Starmer, French President Emmanuel Macron and German Chancellor Friedrich Merz.
Sir Keir said late on Friday that Ukraine's allies remained committed to securing "a just and lasting peace once and for all".
Ahead of the G20 summit, which begins on Saturday in South Africa, the prime minister said he and other world leaders would "discuss the current proposal on the table, and in support of President Trump's push for peace, look at how we can strengthen this plan for the next phase of negotiations".
Trump is not attending the gathering over widely discredited claims that white people are being persecuted in the country.
Separately, Zelensky said he had spoken "for almost an hour" with US Vice-President JD Vance and Army Secretary Dan Driscoll, adding that Ukraine "always respected" Trump's efforts to end the war.
In Washington, Trump warned that Ukraine would lose more territory to Russia "in a short amount of time".
He said it was "appropriate" to give Ukraine until 27 November - Thanksgiving in the US - to agree to the peace deal, but added deadlines could be extended if things were "going well".
Speaking at the White House on Friday, the US president said "we think we have a way of getting peace", adding that Zelensky "is going to have to approve it".
Washington has been pressing Kyiv to quickly accept the plan, and sent senior Pentagon officials to the Ukrainian capital earlier this week.