Rudy Giuliani, U.S. President Donald Trump's personal lawyer, said Monday he could not be absolutely sure Trump did not threaten to cut off aid to Ukraine in a controversial phone call with the Ukrainian president, which is now under congressional investigation.

Asked during Fox Business' "Mornings with Maria" about the content of the July 25 phone call between Trump and Ukrainian President Volodymyr Zelensky, Giuliani first said reports purporting that Trump threatened to cut aid to the country was "a false story," but he later added that he could not be "100 percent" sure Trump did not make the threat.

The Wall Street Journal reported Friday that Trump pressed his Ukrainian counterpart to seek information about business dealings between Democratic presidential candidate Joe Biden's son, Hunter Biden, and a Ukrainian gas company. The information could potentially be damaging to Joe Biden's White House bid.

Trump, who on Friday said it did not matter what he discussed with Zelensky in that "beautiful conversation," appeared to confirm Sunday that he did talk about Biden on the phone.

The president told reporters before departing from White House for events in Texas and Ohio that his conversation with Zelensky was "largely congratulatory" but also about "all of the corruption taking place."

The Wall Street Journal said in the Friday report that Biden, during his trips to Ukraine as vice president, had asked the Ukrainian government to oust former prosecutor general, Viktor Shokin, who had launched an anti-corruption investigation into Burisma Group, a private Ukrainian gas company of which Hunter Biden was a board member during his father's vice presidency.

"It was largely the fact that we don't want our people, like Vice President Biden and his son, creating to the corruption already in the Ukraine," Trump said.

During an event held Jan. 23, 2018 at the Council on Foreign Relations, Biden boasted about pressuring the Ukrainian authorities to sack Shokin by threatening to withhold some 1 billion U.S. dollars in loan guarantees.

"If the prosecutor's not fired, you are not getting the money," Biden said, repeating what he told Ukrainian officials during a trip to the Eastern European country in 2016.

The former vice president urged Trump to release the transcript of the July phone call. "At minimum, Donald Trump should immediately release the transcript of the call in question, so that the American people can judge for themselves," he said in a statement Friday.

"It was the perfect conversation," Trump said of his call with Zelensky as he spoke to reporters Sunday near Houston, Texas. "But we'll make a determination about how to release it, releasing it, saying what we said."