Henry J. Kaufman, chief economist for Salomon Brothers, said yesterday that he believes interest rates will remain stable in the short term and may shoot back up to the high levels of 1981 following renewed economic growth later this year.

That rise may derail "the one thing we're trying to nurture," he warned on NBC's Meet The Press. "The investment boom will capsize," said Kaufman, whose assessments are widely heeded on Wall Street.

In a characteristically gloomy assessment, Kaufman said that Congress and the White House have not sufficiently set aside "strong economic dogmas" to produce the response to the near crisis situation confronting the "fragile" economy.

Presidential adviser Edwin Meese III, appearing on ABC's This Week With David Brinkley show, had a more cheerful forecast about interest rates. Meese said he had heard prominent economists and business people say that they believe rates "will be down in the neighborhood of 14 percent, perhaps lower, in the course of the next quarter to six months. I would certainly hope that's true.

"Frankly I hope they will go lower than that," Meese said. "A real interest rate would be somewhere in the neighborhood of 10 percent . . . I think they will be coming down."

The current prime rate is 16.5 percent, but during 1981 it went over 20 percent.

Meese called on congressional Democrats to back President Reagan's budget plans because "they know this budget will help get interest rates down."

He said that people in decision-making positions were skeptical that interest rates would come down significantly because of concerns that recession will be followed by inflation. In contrast, he said, the White House believes its recovery plan "can produce this recovery without inflation, because we're not going to the big federal spending programs, we're not going to the surges in the money supply--the kind of policies that often in an election year were used in the past and which led us back into inflation."

Kaufman said that the budget deficit in fiscal 1983 could be as large as $150 billion to $175 billion.

He offered his own corrective for the economy's troubles, saying that the pending tax cut should be postponed and that indexation of the tax system and all other indexation in the budget, including that of Social Security benefits, should be removed.

"We're in an unusual time, not in an ordinary cyclical period," Kaufman said. "We're in a time when our economy has become fragile. We must do things that are extraordinary. We must do things that are difficult, and that in some respects are painful."

Kaufman said such pillars of the economic system as the thrift industry, productivity and the liquidity of business institutions have been weakened, leaving the economy shakier than in the previous 30 years.