Treasury Secretary Steven Mnuchin told CNBC on Thursday the administration and congressional leaders are continuing toward resolving an impasse over the debt ceiling and he is confident an agreement will be reached that will ensure the U.S. does not default on its obligations.

"I don't think the market should be concerned," he said. "I think everybody is in agreement that we won't do anything that puts the U.S. government at risk in terms of our issue of defaulting. I think that nobody wants a shutdown in any scenario. So I don't think the market should be concerned, and we're working hard. We'll get there one way or another."

In what he called his "most conservative" scenario, the U.S. could lose its spending ability by early September. At that point, the Treasury would not be able to make payments on its $22 trillion debt load, a potentially catastrophic event that would ripple through financial and world markets.

Both sides have been negotiating on reaching future spending limits and a longer-term agreement on continuing to allow the government the ability to borrow. There have been some indications that an agreement is near, though CNBC's Ylan Mui reported earlier that the two sides remain significantly apart.

In the interview on "Squawk Box," Mnuchin said he has been having "daily conversations" with House Speaker Nancy Pelosi, D-Calif., they have reached an agreement on "top-line" spending numbers over a one- and two-year period, and are now working on "offsets" to put caps on spending.

He added that everybody involved is aware of the risks that the inability to reach a deal would bring.

"I've discussed that with the leadership of both the House and the Senate," he said. "That's why I've encouraged them to raise the debt ceiling before they leave."

Lawmakers plan on leaving for their August recess on July 26.

The Treasury has been using a series of "extraordinary measures" to keep the government running while the spending impasse continues. The measures currently in use entail halting sales of state and local government series Treasury securities, redeeming existing sales and suspending any new investments of civil service and Postal Service pension funds, and suspending reinvestments of the Government Securities Investment Fund and the Exchange Stabilization Fund.

Mnuchin earlier had said that those measures could keep the U.S. afloat into November, but recently shortened the time span.