Interest rates will stay high until the inflationary outlook improves, outgoing Treasury Secretary G. William Miller told the Senate subcommittee on debt management yesterday.

He warned that the high cost of money could choke of economic recovery, and that this would be very disappointing "at a time when there is unused capacity in the economy, both human and physical."

Testifying perhaps for the last time before the Senate panel, Miller asked the subcommittee to raise the limit on government debt to $978.6 billion through next Sept. 30, from the present limit of $925 billion to the end of February. The House already has approved the higher debt limit.

Higher-than-expected interest rates were one factor in pushing up the public sector's borrowing needs, he said. They would add an estimated $3 billion to the cost of servicing debt between October and February.

The Treasury secretary said he had serious doubts about whether the new limit would be adequate for the rest of fiscal year 1981. But he thought that the incoming administration should work out its own debt limit ceiling to correspond to its own budget tax proposals and should present that to Congress.

Meanwhile, raising and extending the present limit would "avoid the need for further congressional action during this session of Congress and will avoid the need for emergency action by Congress on debt limit legislation early next year," he added.

"Tax cuts without immediate commensurate cuts in spending" would increase the government's financing needs, he said, apparently referring to the president-elect's commitment to cut taxes significantly next year.

The Treasury now estimates that the debt subject to limit will be $943 billion by the end of February. If the limit is not raised, the incoming Reagan administration would have to take immediate action to raise it when the new administration comes into office at the end of January.

Total federal demands for new credit, including borrowing to finance off-budget spending, amounted to $70.5 billion in fiscal 1980, or 16.7 percent of all new credit raised in U.S. markets, Miller said. The Treasury expects a similar percentage figure for fiscal 1981.This compares with a 27 percent government chare of all new credit in 1976 and only 6.4 percent in 1979. The figures are heavily influenced by the business cycle.

Miller explained that of the $18 billion increase from the present ceiling of $925 billion, $6 billion came from boosting the cash balances to the desired $15 billion and $12 billion from changed fiscal policy.

The new figures are allowed for in the second budget resolution, whereas the $925 billion limit is in line with Congress' fist budget resolution.

Among the factors pushing up the public debt are the higher interest rates, increased defense spending, a settlement award of $2.1 billion to Penn Central and higher spending by the Housing and Urban development program.

Curbing federal spending should be the highest priority in fiscal policy, Miller said. He expressed disappointment that the Carter administration had not managed to hold down spending and government borrowing more effectively.