President Reagan's annual Economic Report to Congress yesterday called unemployment "the most serious economic problem now facing the United States," but the report rejected government jobs programs--favored by Democrats--as a solution.

The White House has forecast that unemployment will rise further in coming months and still be close to 10 1/2 percent by yearend. But Martin Feldstein, chairman of the Council of Economic Advisers, said yesterday that the forecast may be too gloomy and that unemployment could drop to 9 1/2 percent by the end of the year if the economic recovery has already begun, as some observers believe.

The Economic Report, prepared by the CEA, foresaw "a long period of sustained growth with low inflation" but only a slow reduction in unemployment, to 6 1/2 percent by 1988. It also warned that high budget deficits will hold down investment and could make the recovery "lopsided."

The jobs programs under consideration by the Democrats would add $5 billion to $7 billion a year to federal spending, increasing the deficit unless offsetting cuts were made.

Feldstein, who has stressed the importance of spurring capital investment by business to expand job creation, told the Joint Economic Committee of Congress yesterday that a "balanced recovery . . . requires a sound monetary policy and budgetary changes" to shrink deficits which at present levels would crowd out future investment.

He praised the Federal Reserve's money policy, and said the Fed should aim at broad money growth this year of about 7 percent to 9 percent, before taking account of the enormous shifts in the money numbers caused by the introduction of popular new high-interest bank accounts.

While the money numbers may show huge increases in coming weeks because of the banking changes, the Fed's underlying policy of a gradual deceleration in the money supply has not changed and should not change, Feldstein said.

Calling lower budget deficits the "key" to a healthy recovery, the CEA chairman told reporters it would be better to increase taxes in future years than to have deficits continue "indefinitely." Reagan's new budget has a deficit of $117 billion by 1988.

It would "be better to have a good tax increase than a bad budget deficit," Feldstein said. The Economic Report warned that "a succession of large budget deficits is likely to reduce substantially the rate of capital formation" and to lead to slower long-term growth.

However, the president's adviser said it would be "irresponsible" to raise taxes this year by canceling the third year of the president's multi-year tax cut, as this could threaten to choke off recovery. He also opposed undoing the tax "indexing" provision that is due to come into effect after 1985.

The Economic Report, the first since Feldstein became chairman, acknowledged that the battle against inflation has been painful and costly, in contrast to the administration's early predictions.

However, it called the 1982 decline in inflation "the major economic achievement" of the year, and said policy should continue to be aimed at holding down inflation, while allowing real growth of 4 percent a year on average until 1988.

The adminstration is "ambitious in predicting a sustained expansion without increasing inflation," Feldstein said to the JEC, pointing out that "the two long-lasting expansions of the postwar period were accompanied by increasing inflation."

The Economic Report forecast a slight rise in inflation this year as some commodity prices stop falling and the dollar declines a little. But after that, inflation is expected to decline to 4.4 percent a year by 1988.

In a special section on unemployment, the Economic Report distinguished between "cyclical" unemployment, caused by recession, and "structural" unemployment which cannot be eliminated through overall fiscal and monetary policies without threatening to increase inflation. Only an economic recovery can bring down cyclical unemployent, currently affecting about 5 million people, the report said. It advocated special measures to reduce "structural" unemployment among the longterm unemployed and among young people, including a sub-minimum wage for young people during the summer.

Feldstein said "you can't design a jobs program to hire the 14 million people" who will need jobs in coming years, including those now "cyclically" unemployed and the likely 9 million increase in the labor force.

Congressional support for a public works program would be "not just a waste of $5 billion but a signal to financial markets that Congress can't control spending," he said.

Other special sections dealt with investment and current strains on the world financial and trading system.

The report praised the 1981 business tax cuts and supported further cuts in taxes on capital in order to counteract previous policies which "have tended to alter the allocation of capital investment, favoring housing, consumer durables, and state and local construction at the expense of business investment."

On the international side, Feldstein told reporters it may take five or six years before the world financial system recovers from recent debt problems. The report says recent debt problems that have hurt the ability of developing countries to import have, other things being equal, cut the U.S. gross national product by about .5 percent.