"I think that just looking at the flow of initial claims, that it looks like we're probably going to get close to 20% in the next report, depending on whether the virus has really abated by that point and the economies are really going again", said Mr.
Unemployment soared to 14.7 percent in April - the highest rate since the Great Depression - and analysts predict it will rise still further in May.
That shattered the post-World War Two record of 10.8% touched in November 1982.
President Donald Trump, meanwhile, is not in a rush to sign another trillion-dollar relief bill, despite calls to do so by top Democrats in Congress, Mnuchin and other White House officials have said. Mnuchin appeared to echo that view, saying Sunday: "We're not going to do things just to bail out states that were poorly managed".
White House advisers said Sunday that it is too early to pass additional economic package as Congress has begun preliminary discussions on a fourth such bill.
Mr Mnuchin and Mr Hassett stressed that the jobs market collapse had come as a result of the deliberate shutdown of the USA economy to slow the spread of the coronavirus, not because of structural factors.
White House economic adviser Kevin Hassett also predicted unemployment would hit a "trough" in May or June, with unemployment rates "north of 20%". At the White House, all employees are being tested at least weekly, officials said, and a handful of top aides who regularly interact with the president are being tested daily, they said.
The treasury secretary also warned that joblessness would likely grow in the coming weeks.
Democrats are pushing for another massive relief bill that would include more money for state and local governments, coronavirus testing and the U.S. Postal Service.
Kudlow said he took part in a Friday conference call with House politicians from both parties, and that he planned to do the same on Monday with members of the Senate.
"We're collecting ideas for next steps, which will undoubtedly be data-driven", Kudlow said.
The United States will need more tests before schools can reopen later in the year, said Senator Lamar Alexander, chairman of the Senate Health, Education, Labor and Pensions Committee. There is now no coronavirus vaccine.
Neal Kashkari, president and CEO of the Federal Reserve Bank of Minneapolis, told ABC's "This Week" he would welcome a robust recovery.
"Unfortunately, you can't do everything, so these numbers are going to be very poor, but I would not lose hope, because I do think at the back end of the year, we're going to see a rebound", he added. But people will be able to go into stores, some of them will have reservations when they go in, but businesses will be able to reopen, he said.