The Texas senator, who challenged Mr Trump to be the Republican nominee in 2016, was mocked for saying he believed there was “considerable evidence” that Ukraine meddled in the most recent presidential election.
The US intelligence community has concluded that Russia, not Ukraine, interfered in the 2016 election and senior officials have said it is a “fictional narrative” to suggest Ukraine was involved.
NBC host Chuck Todd questioned Mr Cruz on why he would trust Mr Trump’s claims about Ukraine after he was involved in a bitter feud with the president during the 2016 campaign.
“You went through a primary campaign with this president. He launched a ‘birtherism’ campaign against you, he went after your faith, he threatened to ‘spill the beans’ about your wife about something…” Mr Todd said.
“Is it not possible that this president is capable of creating a false narrative about somebody in order to help him politically?”
However, Mr Cruz rejected that suggestion because Mr Trump released a memorandum of his call with Ukrainian president Volodymyr Zelensky which he claims proves his innocence.
The president is accused of withholding military aid and the offer of a White House meeting to Ukraine to pressure Mr Zelensky into announcing an investigation into his 2020 election rival Joe Biden.
Although he has denied any wrongdoing, multiple US officials have come forward with concerns about his conduct.
In response to the allegations, multiple Republican senators and members of Congress have spread baseless or discredited conspiracy theories about Ukraine’s role in the 2016 election and Mr Biden’s son Hunter.
Mr Nadler, who is the chairman of the House Judiciary Committee investigating Mr Trump, replied: “I don’t know. The president, based on his past performance, will do everything he can to make it not a fair election and that is part of what gives us the urgency to proceed with this impeachment”
The chairman also said on Sunday that a vote in Congress on impeachment charges against the president could take place this week.
If the articles of impeachment are passed, Mr Trump will be tried in the Republican-controlled Senate.
A two-thirds majority of senators must vote to convict Mr Trump for him to be removed from office.