High interest rates will add more than $10 billion to federal spending next year, pushing it over $700 billion even after the budget cuts the president has called for and Congress has approved, the administration said yesterday.

But the budget deficit in 1982 will be slightly lower than first projected, at $42.5 billion, as higher tax revenues offset the increased spending, the White House said in its midyear budget review.

The new estimates also show that President Reagan must make about $10 billion more in spending cuts than first projected for 1984 if he is to balance the budget in that year as promised. That means some $55 billion will have to be carved from 1984 spending.

The administration has not yet identified where $44.2 billion of these cuts will be made. It says $10 billion will come from the cuts it proposed in Social Security costs in May.

The new report has the administration sticking closely by its estimates for the 1981 and 1982 budget deficit, despite higher spending forecast. Presidential economic adviser Murray Weidenbaum also stressed to reporters yesterday that "this administration is determined to balance the budget by 1984."

As reported in The Washington Post last week, Reagan officials now see higher interest rates, more growth and lower inflation this year than they expected in March.

The economy is now virtually stagnant, but according to the forecasts will pick up next year. Output is expected to rise 5.2 percent from the fourth quarter of this year to next, and consumer prices only 6.2 percent.

Growth for this year is now put at 2.6 percent, up from a first estimate of 1.1 percent. Weidenbaum said, however, that the economy was now "soggy" and unemployment would likely rise slightly in the next few months.

The administration predicts that interest rates will fall soon from their present heights. But short-term rates will be above 10 percent this year and next, the forecast says. Three-month Treasury bills are now expected to average 13.6 percent this year, and 10.5 percent next.

The administration still predicts strong growth, combined with falling inflation, for the later years of its forecast. By 1984 consumer prices are projected to be rising by just over 5 percent, with real growth at 4.5 percent and unemployemnt at 6.2 percent.

Higher tax revenues in 1981 and 1982, a result of delaying a cut in individual taxes from July to October this year, will offset the effect on the deficit of increased spending, the review said.

The revised figures show a deficit of $55.6 billion in 1981, very close to the original projection the administration made in March, with spending of $661 billion.

Spending in 1982, assuming $3.8 billion in Social Security cuts, is now put at $704.8 billion, up from the $695 billion projected in March, and incorporated in the first budget resolution. Revenues are projected at $662.4 billion, up $12 billion from March.

Reagan attacked President Carter for raising taxes to offset spending overruns. Budget Director David A. Stockman yesterday denied that the administration had changed its position on the timing of this year's tax cut in order to offset higher spending, even though the delay has that effect. He also said that the administration would "absolutely not" attempt to "balance the budget [in 1984] by raising taxes."

He said that one reason for enacting a three-year tax bill, which Reagan wants but critics fear could be inflationary, is to create added pressure for more spending cuts, in order to close the budget deficit.

An unexpected boom in the first three months of the year has held down 1981 spending by cutting payments on unemployment benefits by $4.7 billion, the review said. On the other hand, higher interest rates have added nearly $7 billion to spending in 1981, and $10.3 billion in 1982.

Other changes include $2.7 billion more in 1981 spending on farm price supports. Stockman commented that the administration hoped to speed up sales of grain from the Commodity Credit Corp.

Paradoxically, a more optimistic outlook for inflation, particularly oil prices, will make it harder to balance the budget in 1984. By then lower inflation will cut $12 billion from estimated tax receipts, Stockman said yesterday, $7.2 billion coming from a cut in the revenues from the windfall profit tax.

The administration now assumes that the budget will be balanced with 1984 spending at $758.5 billion, instead of the $770 billion assumed in March. The inflation improvement will cut $5.2 billion off spending on indexed programs in 1984, Stockman said. However, this is partially offset by the continued effect of high interest rates of the cost of servicing the public debt.