The Treasury Department, free to return to the capital markets again, announced yesterday that it will raise at least $15.5 billion in new money between Oct. 16 and 24.

The government had to postpone two debt sales this week because any sale of new securities would have pushed the total federal debt above the legal limit of $1.573 billion.

Hours after the Senate raised the debt ceiling to $1.823 trillion yesterday afternoon, the Treasury announced that it would reschedule the two postponed offerings and also announced a new one.

Treasury officials are faced with raising between $55 billion and $60 billion between now and the end of the year, and are concerned that the canceled offerings will force the agency to raise so much money in such a short time that the government will have to pay more in interest.

"It's difficult to project exactly how much this congestion will cost the Treasury," a spokesman for the agency said.

The Treasury actually will sell far more than $60 billion in debt securities in the current quarter; in addition to raising new money, it will have to repay billions of dollars of debts that mature between now and Dec. 31.

According to one Treasury estimate, to pay its bills on time the government will be forced to raise $42 billion in the next four weeks. Only a few years ago, the Treasury's total borrowing requirements for a year were less than $42 billion.

The government could have continued to pay its bills for a few days more had Congress failed to pass the increase in the debt ceiling yesterday.

But officials said that at some point in the next two weeks, expenses would have exceeded revenues and the government would have had to stop writing checks.

Because Congress had voted to close the session at midnight Friday, if the Senate had failed to pass the increase in the debt ceiling yesterday, President Reagan probably would have been forced to declare an emergency and reassemble the legislature.

The debt ceiling got caught up in end-of-session, election-year politics. But its passage yesterday cleared the way for a final adjournment of the 98th Congress.

The Treasury announced yesterday that it would auction $5.5 billion of seven-year notes on Oct. 16; $4 billion of 20-year bonds on Oct. 23, and $6 billion of three-year, 11-month notes on Oct. 24.

The agency also can sell up to an additional $1 billion in the notes to foreigners.

Besides postponing the sales of the seven-year notes and the 20-year bonds this week, the agency reduced by $800 million the amount of bills it sold at its regular weekly auction.

The $800 million represented the new money the agency planned to raise in the regular sale of short-term securities.

In the first nine months of 1984 the federal government raised $128 billion of new funds.

Under governent accounting policies, the final three months of calendar year 1984 represent the first three months of the federal government's 1985 fiscal (or spending) year.