Mr Cuomo informed the congressman that the man in question, Dmitri Alperovitch, is an American citizen who was born in Moscow, Russia.
“He’s not Ukrainian… and even if he were, that’s what you’re going to hang it on?” Mr Cuomo asked.
“Your head of national security, Tom Bossert, said that that was a joke. You heard testimony from experts saying it’s a joke. The intel community says it’s not true. Mueller said it’s not true.”
Mr Weber then tried to push a debunked rumour that CrowdStrike hid physical evidence which showed Ukraine, not Russia, interfered in the 2016 presidential election.
“There was no server, they operated in a cloud system. There is no server to steal,” an exasperated Mr Cuomo replied.
The congressman conceded there was no server but insisted the president just wanted to see an investigation into the cybersecurity company.
“It was investigated,” the CNN host responded.
“What he went to Zelensky [Ukraine’s president] with was a conspiracy theory that there is some missing server when there is no physical server. Crowdstrike and the FBI both said it.”
A memorandum of Mr Trump’s phone conversation with Volodymyr Zelensky on 25 July showed that Mr Trump asked the Ukrainian president for a “favour” in relation to CrowdStrike.
“I would like you to find out what happened with this whole situation with Ukraine, they say Crowdstrike,” Mr Trump said.
“The server, they say Ukraine has it.”
The US intelligence community and the Mueller report both concluded that Russia interfered in the 2016 election and a recent investigation by the Republican-controlled Senate Intelligence Committee found no evidence of similar interference by Ukraine, according to Politico.
In November, Russia’s president Vladimir Putin appeared to gloat about Mr Trump pushing the false theory that Ukraine attempted to swing the election.
“Thank God, no one is accusing us of interfering in the US elections anymore; now they're accusing Ukraine,” Mr Putin said.
Mr Trump is accused of withholding the offer of a White House meeting and the release of military aid to Ukraine to pressure Mr Zelensky into announcing an investigation into his 2020 election rival Joe Biden.
He has denied any wrongdoing, despite multiple US officials coming forward with concerns about his conduct.
During a recent impeachment hearing, Fiona Hill, Mr Trump’s former top Russia adviser, warned Republicans were spreading conspiracy theories pushed by Russia.
“Some of you on this committee appear to believe that Russia and its security services did not conduct a campaign against our country and that perhaps, somehow, for some reason, Ukraine did,” Ms Hill told Congress.
“This is a fictional narrative that has been perpetrated and propagated by the Russian security services.”
On his CNN show, Mr Cuomo attempted to convince Mr Weber to admit that Ukraine was not involved in election interference in 2016.
“If you are going to try to defend the president by running a conspiracy theory that Ukraine did something not Russia, you are undermining American institutions and faith in fact just out of political convenience,” Mr Cuomo said.
Mr Weber then conceded that the presenter was right about Russia interfering in the election but he maintained Mr Trump’s concerns about corruption in Ukraine were legitimate.