WASHINGTON (AP) — Treasury Secretary Henry Paulson sought to reassure an anxious public Sunday that the banking system is sound, while also bracing people for more troubled times ahead.

‘‘I think it’s going to be months that we’re working our way through this period — clearly months,’’ he said.

Paulson said the number of troubled banks will increase as they struggle to cope with big losses on bad mortgages. The government this month took over IndyMac after a run led it to become the largest regulated thrift to fail.

‘‘Of course the list is going to grow longer given the stresses we have in the marketplace, given the housing correction. But again, it’s a safe banking system, a sound banking system. Our regulators are on top of it. This is a very manageable situation,’’ he said in broadcast interviews.

Paulson used appearances on the Sunday talk shows to tell people that deposits up to $100,000 are fully insured.

He said no one has lost a single penny on an insured deposit in the 75 years that the Federal Deposit Insurance Corporation has operated.

‘‘We’re going through a challenging time with our economy. This is a tough time. The three big issues we’re facing right now are, first, the housing correction which is at the heart of the slowdown; secondly, turmoil of the capital markets; and thirdly, the high oil prices, which are going to prolong the slowdown,’’ he said.

‘‘But remember, our economy has got very strong long-term fundamentals, solid fundamentals. And you know, your policy-makers here, regulators, we’re being very vigilant.’’

Paulson said he hoped Congress soon would approve his plan to help shore up Fannie Mae and Freddie Mac, the government-sponsored mortgage companies

‘‘I’m very optimistic that we’re going to get what we need from Congress here, because Congress understands how important these institutions are,’’ Paulson said.

The House plans to vote Wednesday on a housing bill that is expected to include a rescue for Fannie Mae and Freddie Mac. The companies’ shares have plummeted because of fears about their financial stability. Fannie Mae and Freddie Mac are private, but they were created by Congress to encourage homeownership by buying mortgages from banks. The two hold or guarantee more than $5 trillion in home loans — almost half of the nation’s total.

‘‘Our first priority today is the stability of the capital markets, the stability of the system. And these institutions have investors all around the world … and those investors need to know that we in the United States of America understand the importance of these institutions to our capital markets and to our economy and to our housing market,’’ he added.

Paulson acknowledged the U.S. is continuing to lose jobs, though he said the $168 billion economic relief plan approved this year has created jobs that would not otherwise exist. The plan included tax rebates for people and tax breaks for businesses.

Democratic leaders, including presidential candidate Barack Obama, are pushing for a second, smaller, economic installment. Paulson said he did not want to speculate about that idea.

‘‘I’m focused on this stimulus package. It’s made a difference in the second quarter. It’s going to make a difference in the third quarter. We need to watch this very carefully,’’ he said.

‘‘Right now we’re going through a tough period. There is no doubt about it. But the stimulus plan is making a difference,’’ he said.

The second-ranking House Republican, Rep. Roy Blunt of Missouri, said he was ‘‘open-minded’’ about a follow-up aid plan. ‘‘If they bring things to the table they know the president’s not going to do, that has very little to do with stimulating the economy. It’s all about a political discussion between now and the election,’’ he said.

Paulson appeared on ‘‘Face the Nation’’ on CBS and ‘‘Late Edition’’ on CNN. Blunt was on CNN.