President Donald Trump's personal lawyer Rudy Giuliani said Friday that he is no longer planning to travel to Ukraine to urge the president-elect to push forward with investigations that he anticipates could help Trump's re-election campaign.

Speaking on Fox News to host Shannon Bream, Giuliani said he believes he faced an unspecified political trap if he proceeded with the much-criticized trip that would have focused on an investigation involving former Vice President Joe Biden, who's running for the Democratic presidential nomination.

"I’m not going to go because I think I’m walking into a group of people that are enemies of the president," Giuliani said on Fox News. " ... I think this was a set-up."

The trip was revealed in an interview with The New York Times published Thursday. He told the newspaper, "We're not meddling in an election, we’re meddling in an investigation, which we have a right to do."

According to The Times, Giuliani planned to ask Volodymyr Zelensky, the Ukrainian comedian elected last month to lead the nation, to move ahead with probes involving the son of potential Trump rival Joe Biden as well inquiries related to special counsel Robert Mueller's investigation into Russian interference in the 2016 campaign.

"There's nothing illegal about it," he told the paper.

But, the former New York City mayor allowed in the interview, "Somebody could say it's improper."

Democrats quickly did.

“We have come to a very sorry state when it is considered OK for an American politician, never mind an attorney for the president, to go and seek foreign intervention in American politics,” said Rep. Jerrold Nadler, D-N.Y., chairman of the House Judiciary Committee, to reporters Friday.

Rep. Adam Schiff, chair of the House Intelligence Committee, tweeted that Giuliani's efforts were not only improper, but "immoral, unethical, unpatriotic and, now, standard procedure."

Giuliani told The Times Thursday that Trump fully supported his plans.

"The President is openly asking a foreign government to investigate his political rival. This is next level," Sen. Chris Murphy, D-Conn., tweeted Friday.

Explain to me why Biden shouldn’t be investigated if his son got millions from a Russian loving crooked Ukrainian oligarch while He was VP and point man for Ukraine. Ukrainians are investigating and your fellow Dems are interfering. Election is 17 months away.Let’s answer it now https://t.co/FT34kX7Pst — Rudy Giuliani (@RudyGiuliani) May 10, 2019

Giuliani tweeted back, "Explain to me why Biden shouldn’t be investigated if his son got millions from a Russian loving crooked Ukrainian oligarch while He was VP and point man for Ukraine."

In a text message, Giuliani told NBC News that what he had planned was "perfectly legal" since it would have involved an investigation. The 2020 "election is 17 months away," he wrote.

In recent days, Giuliani has repeatedly alleged a conspiracy involving the former vice president, who has emerged as the early front-runner in the race to be the Democratic nominee. In an interview with NBC News earlier this week, Giuliani said he stumbled upon the story by accident as he was investigating a claim he'd heard about Democratic National Committee officials "using the American embassy in Ukraine as their focal point to get dirt on Trump" and former Trump campaign chairman Paul Manafort, who earned millions working for a corrupt pro-Russian political party in Ukraine for nearly a decade.

"All of a sudden, as I'm interviewing these people, they tell me the Biden story," Giuliani said.

The "Biden story" involves the then-vice president's 2016 call for Ukraine to crack down on corruption, including removing a Ukrainian prosecutor, Viktor Shokin, seen as ineffective. As Giuliani has noted, one of the cases that Shokin had been investigating involved a company called Burisma Holdings. Biden's son Hunter Biden was on the board of the company at the time.

Hunter Biden and Joe Biden at the World Food Program USA's Annual McGovern-Dole Leadership Award Ceremony at Organization of American States on April 12, 2016, in Washington. Teresa Kroeger / Getty Images file

But Bloomberg News, citing documents and an interview with a former Ukrainian official, reported earlier this week that the Burisma investigation had been dormant for over a year when Biden called for the crackdown on corruption. PolitiFact, meanwhile, reported that it found no evidence to "support the idea that Joe Biden advocated with his son's interests in mind."

Giuliani has said, and The Times has reported, that Ukrainian prosecutors have reopened the Burisma investigation, but a spokesperson for the Ukrainian prosecutor's office told Bloomberg that it had not done so.

That spokesperson did not respond to a request for comment from NBC News.

Hunter Biden, who stepped down from Burisma's board last month, told The Times, "At no time have I discussed with my father the company's business, or my board service."

Giuliani told NBC News, "I assure you I am not trying to take him [Biden] out. I'm actually — he won't appreciate it — but I'm doing him a favor by trying to get it investigated now. Because it wasn't going to live through November of next year."

But on Fox News on Friday, he said, "I am actually quite confident that facts with regard to vice president -- former vice president -- Biden are so compelling that there’s no way that he gets from here to the election without this being investigated."

The DNC has repeatedly denied working with the Ukrainian government to obtain dirt on Manafort. The incriminating Ukrainian information about Manafort that emerged during the campaign — a ledger showing $12.7 million in unreported payments from a Russia-backed Ukrainian political party — was from public records. However, Ukraine's current top prosecutor has reportedly opened an investigation into whether the Manafort information was released in order to help Hillary Clinton's campaign.

Manafort, 70, is serving a seven-and-a-half year federal prison sentence for undisclosed lobbying work in Ukraine, as well as tax and bank fraud — charges that were brought as part of Mueller's investigation but were unconnected to Manafort's work with the Trump campaign.

The New York Times previously reported on Giuliani's interest in the Biden and Manafort-related inquiries as well as his meetings with Ukrainian officials about the probes. Giuliani said then he'd been keeping the president apprised of his efforts.

Trump spoke about the Biden story in an interview with Fox News last week.

“I’m hearing it’s a major scandal, major problem,” Trump said, adding, “I hope for him it is fake news. I don’t think it is.”