The U.S. unemployment rate will rise swiftly and dramatically as the coronavirus brings the American economy to a stop, former top White House economic advisor Gary Cohn told CNBC on Thursday.

"I believe that we are going to have massive unemployment very, very quickly," Cohn said on "Squawk Box."

Cohn's comments came shortly after the Labor Department said jobless claims rose to 281,000 last week, an increase of 70,000 from the week prior.

However, the former Goldman Sachs president is not alone in forecasting a continued jump in unemployment. Ian Shepherdson, founder and chief economist of Pantheon Macroeconomics, told CNBC earlier that he thought next Thursday's jobless claims could be around 2 million.

"I hope all of our predictions are wrong but you cannot work today. Even if you want to go out and work, you're not allowed to work," Cohn said. "If you're an Uber drive and you're out there trying to pick up fares, there's no fare to pick up. In essence, you're de facto unemployed. Not because you want to be unemployed, you're unemployed because there's no revenue opportunity for you."

Like the overall economy, the U.S. job market was on solid footing before COVID-19 upended daily life.

The nation's unemployment rate in February was 3.5%, matching a roughly 50-year low. The country added 273,000 jobs last month before the most serious impact from the pandemic began taking place.

Cohn said Congress needs to urgently pass economic relief measures, adding he's in favor of broad actions that could be approved quickly.

"I would love to see more targeted to people that are unable to work and don't have the financial means. I just don't know if we have a enough time to go through the proper detail and get it to the right people," he said.

"If we're going to err on giving it too many people or too few people, I'd rather give money to too many people at this point and make sure we at least keep people in a position where they can feed their families and they can be in a position to help us recover the economy."

Cohn resigned from the Trump administration about two years ago after losing the president's ear on avoiding trade tariffs and trade wars.

On Thursday, he said he would like to be as helpful as possible to President Donald Trump. "I'm in touch was some of my former colleagues in the White House ... and I continue to reach out."