President Reagan last night defended a move in the Senate to find $40 billion in savings in the Social Security system but left the door open for a compromise with House leaders who have said any cuts in cost of living increases are unacceptable.

The president repeated assurances Social Security beneficiaries will get the 7.4 percent increase due in July but he said, for the first time, that it may become necessary in the future to temporarily cut back on cost-of-living increases although he considered that unlikely.

Reagan accused the Democrats of distorting a Republican proposal to reduce Social Security savings by $40 billion over the next few years and criticized them for refusing to face up to the financial problems of the Social Security system.

He said they used "falsehoods" and "demagoguery" to "terrorize" Social Security recipients and turn his proposals for dealing with the system's problems into a "political football."

He indicated, however, that he would not stand in the way of a Hill move to eliminate the $40 billion Social Security saving that was proposed last week. He described the proposal this week by House GOP leaders to separate the sensitive and politically volatile Social Security issue from the budget debate was "an interesting idea" but he declined to support it.

He said the $40 billion figure was the amount by which the Social Security fund was insolvent.

"In all of the demagoguery and all of the outright falsehood that have been uttered about this . . . the Senate put the number into the budget only because they believe that it was honest to call attention to the fact that that is the figure by which and the amount of which Social Security is insolvent--that this must be corrected before the end of next year."

The economy will begin to turn around, Reagan said, once Congress approves a budget and the second phase of his program of tax cuts goes into effect in July.

But, he said it may not be until later this year that the post-World War II record unemployment begins to come down.

But he stood firm in saying that he did not intend to take any government action to reduce unemployment, arguing that this had been the mistake of previous administrations and had served only to plunge the country into a series of recessions, each worse than the one preceding.

He said that interest rates would begin to come down once the money markets understood that his administration was serious about reducing government spending and the size of the deficit but warned that expecting "instant recovery" was simply "asking too much."

Asked why he had begun paying "sudden attention" to black Americans, Reagan responded tartly, "I've been doing things like that all my life. You just haven't been paying attention."

Reagan said he had gone to visit a black suburban Maryland family after reading of cross-burnings on their lawn because he "was incensed that that still happens. I wanted to tell them that government doesn't feel that way."

He said he had wanted to visit the family without the press but that his aides had told him that if he did that, reporters would "never trust me again, you'd start spying on me and you'd never let me out of sight."

Reagan repeated that he had not known that segregated schools still existed when he issued an order that had the effect of restoring their tax exempt status.

In discussing Social Security, Reagan said that while he believed that current recipients should have their basic benefits protected, he expressed concern that young people now paying high taxes into the system may never get back the benefits they are putting in. He said he felt they would be far better off if they were permitted to use that money to buy a private retirement policy.

What he did not say was that if that is done, the current problems of the Social Security trust fund would be further exacerbated.

On other domestic issues, Reagan said:

The government cannot "put itself into the business" of using taxpayers' money to bail out companies, such as Braniff International airline, that go broke. He said he believed the main responsibility of government was "to create a better business climate" and to bring interest rates down.

He had written letters to 5,000 business executives, asking them to provide summer jobs for disadvantaged youth and he said there is $22 billion in the current budget to deal with the problems of those out of work.

Indicated he did not support eliminating the progressive income tax system and substituting a flat rate tax as some of his advisers have proposed.

Reagan said he thought such a proposal could mean that individuals, no longer able to take income tax deductions, would not contribute to the arts and medical and educational institutions.

After the press conference, Reagan was asked if had followed the news of the trial of his assailant John W. Hinckley Jr. The president said he did read some about it but not much. He expressed sympathy for Hinckley's parents.