KYIV, Jan 8 (Reuters) - Ukrainian President Volodymyr Zelenskiy said on Thursday the text of a bilateral security guarantee between Kyiv and Washington was "essentially ready" to be finalised with U.S. President Donald Trump.

As a cornerstone of any post-war settlement, Ukraine has sought strong guarantees which commit the U.S. and other Western allies to come to Ukraine's aid if Russia invades again.

Ukrainian and U.S. envoys, joined by a coalition of Ukraine's allies, have been negotiating in Paris this week to iron out remaining disagreements in a peace framework Washington is seeking to thrash out with Kyiv before presenting it to Russia. On Tuesday, the U.S. endorsed the idea of providing security guarantees for Ukraine for the first time.

"The bilateral document on security guarantees for Ukraine is now essentially ready for finalisation at the highest level with the president (Trump)," Zelenskiy said in a post on X.

He said Wednesday's meetings of Ukrainian and U.S. representatives in Paris addressed "complex issues" from the framework under discussion to end the nearly four-year war, and that Kyiv had presented its solutions for these.

The Ukrainian president called for more pressure on Russia after further Russian missile attacks on energy infrastructure on Wednesday, arguing that the credibility of future security guarantees must be demonstrated by a response at this stage.

Under Trump, Washington has shifted its position from an outright supporter of Kyiv to a broker leaning on both sides to agree a peace, and will try to get Moscow to sign up to the deal it negotiates with Ukraine.

Zelenskiy has said that while the framework is 90% agreed, thorny issues remain around control of the Zaporizhzhia nuclear plant as well as Russian demands on Kyiv to cede a strategically significant slice of territory in eastern Ukraine that Moscow has been unable to capture in almost four years of war.

"We understand that the American side will engage with Russia, and we expect feedback on whether the aggressor is genuinely willing to end the war," Zelenskiy wrote on X.

He said the teams also discussed documents dealing with Ukraine's post-war recovery and economic development.

The World Bank last year estimated the cost of Ukraine's reconstruction and recovery at $524 billion, while the Trump administration has sought to leverage economic benefits and privileged post-war access for the U.S. in Ukraine.

(Reporting by Kyiv newsroom and Max Hunder in London; editing by Louise Heavens and Mark Heinrich)