Making no mention of the scandal in his remarks, Pompeo said on Friday: "Today I'm here with a clear message: The US sees that the Ukrainian struggle for freedom, democracy and prosperity is a valiant one. Our commitment to support it will not waver."
Democrats in the US however, believe otherwise, reports Efe news.
The House has already concluded that Trump tried to solicit foreign interference in the upcoming 2020 presidential elections by withholding $400 million in military aid to Ukraine and conditioning Zelensky's visit to the White House on a request that Kiev investigate presidential hopeful Joe Biden's son Hunter, for alleged corruption.
Trump's trial is now in the Senate.
Back in Kiev, the politic could not avoid the issue when it came to the question and answer session.
"No, there's no condition if the nature you described for President Zelensky to come to Washington and have that visit, it's simply not the case. We'll find the right time, we'll find the appropriate opportunity," Pompeo said.
"We want to make sure that it happens at a time when there's substantial progress, things that we can deliver between the two of.
"President Zelensky will be welcome to come to Washington when we have an opportunity to do good things for both the Ukrainian and the American people," he added.
Zelensky, a former TV star who became President in May 2019, echoed Pompeo's statement and said he was ready to go to Washington whenever it was possible.
He emphasized the "excellent" bilateral relations between the US and Ukraine, stressing that he did not think they would be affected by the Trump impeachment trial.
Trump has defended his actions, saying the aid - eventually released in September 2019 - was withheld due to his frustration with what he considered to be an insufficient amount of monetary assistance provided to Ukraine by other countries.
He said the transcript of the phone call with Zelensky proved his innocence.
A second article of impeachment accuses the president of "obstruction of Congress", for directing executive branch agencies, offices and officials not to comply with subpoenas seeking documents and testimony deemed vital to the House's inquiry.
The trial looks set to end in the President's acquittal due to the Republicans - who hold the majority in the Upper House, where a two-thirds vote is required for impeachment - closing ranks behind their leader.
Pompeo is due to continue his tour with a trip to Kazakhstan on Saturday.
( With inputs from IANS )