President Trump's personal attorney Rudy Giuliani promised to release more damaging information on former Vice President Joe Biden, his son Hunter, and their connections with China and Ukraine.

Giuliani, the former mayor of New York City, appeared on Fox Business's Mornings with Maria with host Maria Bartiromo on Monday morning. Giuliani asserted that media coverage of a brewing scandal involving Trump and Ukraine will hurt Biden's presidential campaign more than Trump.

A whistleblower report filed by someone in the intelligence community allegedly says Trump attempted to set up a quid pro quo deal with the Ukrainian president to investigate whether Biden, as vice president, intentionally pushed Ukraine to fire its top prosecutor because the official was investigating Biden's son.

"It's the only way you can get this out. I mean, the only way [the media] would cover this story is by punching the president in the face, and then the president deflects the punch — which he's done. The story has come way down from what it was. And then [Trump] hits them with a right hand that's much more powerful," Giuliani said.

While Congress pressures Trump to release the whistleblower report to the public, reporters are questioning Biden about his past dealings with China and Ukraine when his son was working with those governments in a private capacity.

"Biden was asked about it for the first time on Saturday. Biden was asked about it on Sunday. You start asking Biden, he's going to fall apart," Giuliani said. "It's not over. There's a lot more evidence I'm going to put out. I put one out today: money laundering. I got a bigger one for tomorrow. I got a bigger one for the day after."

"If they can escape China, we literally don't have a system of justice left in this country," Giuliani continued. "$1.5 billion when you are negotiating with China on sensitive issues, and your family gets enriched with an investment in a private equity fund, now why would China give the money to a drug-challenged private equity owner except to influence his father?"

Giuliani's comment on Hunter Biden being "drug-challenged" refers to Hunter's admitted past use of drugs for which he has undergone rehab.

[Also read: MSNBC analyst calls Giuliani 'drunk grandpa' and says he 'needs to be pulled off to hospice']