Treasury Secretary Scott Bessent said on Sunday that he was confident the Trump administration would be able to reach deals with some countries before the deadline on Tuesday for steep tariffs would take effect.

But he also held out the possibility that the deadline could be extended to Aug. 1 for countries seeking to reach deals.

“There’s a lot of foot dragging on the other side, and so I would expect to see several big announcements over the next couple of days,” Mr. Bessent said on CNN’s “State of the Union.” He added, “We’re going to be very busy over the next 72 hours.”

In addition, Mr. Bessent said that the administration would begin informing countries about the tariff rates they could face if they did not quickly reach trade agreements with the United States.

“President Trump’s going to be sending letters to some of our trading partners, saying that, if you don’t move things along, then, on Aug. 1, you will boomerang back to your April 2 tariff level,” Mr. Bessent said. “So I think we’re going to see a lot of deals very quickly.”

Mr. Trump said late Sunday, in a post on social media, that the United States would be delivering letters beginning Monday at noon.

The president also said that any country aligned with “the anti-American policies of BRICS,” an acronym for a group of countries that includes Brazil, Russia, India, China and South Africa, will be charged an additional 10 percent tariff. He did not provide any additional details.

Mr. Bessent’s and Mr. Trump’s comments came just three days before a 90-day pause on the president’s steepest levies is set to expire.

Mr. Trump first mentioned the possible Aug. 1 extension in comments to reporters on Air Force One on Friday night.

“It’s not a new deadline,” Mr. Bessent said Sunday. “We are saying this is when it’s happening. If you want to speed things up, have at it. If you want to go back to the old rate, that’s your choice.”

Mr. Trump announced his so-called reciprocal tariffs, in early April, only to suspend them shortly after, when the threat of the steep duties roiled global financial markets.

So far, the United States has reached preliminary trade deals with Vietnam and the United Kingdom, far from Trump’s goal of 90 deals in 90 days.

Mr. Bessent said he was confident that the administration would be able to reach deals within the next few days once the letters were sent out. “We have the leverage in this situation,” he said.

Tyler Pager contributed reporting.