President Reagan is trying to use his celebrated powers of persuasion to convince business leaders who have backed him in the past that they should rally behind his latest budget proposal despite the difficulties it faces in Congress.

In the face of prominent GOP congressional defections from his budget and high interest rates, which Reagan acknowledges are slowing economic recovery, the president is trying to convince businessmen, especially the investment bankers with whom he is to meet Thursday, that they should lower interest rates for political reasons even if they are unwilling to do so for economic ones.

"We recognize that bankers have many reasons to feel that the current interest rates are justified and why market forces, including the deficits, are terribly important to them," a senior White House official said yesterday. "But we think it's important to enlist their support. If the bankers come out of the White House on Thursday and say the president's budget should be passed, that's a major step forward."

In recent weeks Reagan has praised the isolated actions of Indiana and Illinois banks that acted on their own to make loans available below the prevailing interest rates. So far he has been unable to persuade any of the country's biggest banks to do the same.

The president's message, White House communications director David R. Gergen said yesterday, will be to tell the bankers that the administration is "doing everything we can to lower inflation, and now we're asking that you do all you can to lower interest rates."

Gergen said that Reagan recognizes that "A major reason why interest rates haven't followed inflation on a downward slope is the fear that Washington won't hold the line on deficits. . . . Everyone feels that a major interest in interest rates is psychology."

But there were indications yesterday that the hold-the-line psychology the administration is trying to induce may have backfired.

A few hours after business leaders left the White House making guarded expressions of support for a Republican Senate budget proposal Reagan embraced in the Rose Garden last week, House Minority Leader Robert H. Michel (R-Ill.) rejected it, even though it is a compromise the president is presenting as an emblem of GOP unity.

Michel's statement was hardly the sort to excite enthusiasm among the business leaders with whom Reagan met yesterday, some of whom were already undecided on whether they preferred the GOP plan or a Democratic alternative.

Yesterday Reagan won some predictable support in the first of three days of meetings with 100 business leaders.

"We'll crank up our phone banks," said Bernie O'Keefe, vice chairman of the National Association of Manufacturers.

But Alexander Trowbridge, president of the same organization, said he supported the objectives of both the president's plan and the Democratic alternative, and said, "I think it's important that partisanship be set back a pace . . . . "

Paul Thayer, chairman of the U.S. Chamber of Commerce, offered low-key backing for the White House proposal, and John M. Albertine of the American Business Conference said he "vigorously supported" the president's position.

White House deputy press secretary Larry Speakes said that business leaders were generally supportive, but had raised questions about the new revenues Reagan said he will seek in an effort to lower the deficit.

Speakes said the president told them that he was "against tax increases as much as you are," and promised that he would not do anything to undo the business incentive taxes Congress passed last year.