An article in Friday's editions incorrectly reported that the American Stock Exchange had urged President Reagan to make changes in his economic recovery program. The exchange has taken no position, although its president, Arthur Levitt, has done so.

President Reagan, plainly annoyed that business support for his economic program is eroding, yesterday appealed to the National Association of Manufacturers to stick with him, saying this is not the time for "last-minute haggling or displays of blatant self-interest."

At a luncheon here, Reagan told a friendly audience of several hundred NAM members, "Let me be honest with you . . . and tell you I've been a little disappointed lately with some in the business community who have forgotten that feeding more dollars to government is like feeding a stray pup. It just follows you home and sits on your doorstep asking for more."

In recent weeks, several influential business organizations have urged the president to alter his economic program by raising taxes and restraining his planned defense buildup in order to trim the huge budget deficits now in prospect. Among the groups jumping ship have been the Business Roundtable, the National Association of Home Builders, the American Bankers Association and the American Stock Exchange.

But Reagan's plea to the NAM was successful. After a two-hour meeting of its executive committee later in the day, president Alexander B. Trowbridge issued a statement saying the NAM "continues to strongly support the president's economic recovery program."

The president's expression of annoyance with business groups came only a day after he accused the television networks of contributing to the recession by stressing factory layoffs and other "downbeat" news. Yesterday Reagan indicated he was not trying to pick a fight with the media but he repeated his contention that "a continuing drumbeat" of news about the recession was prolonging it.

At an NAM breakfast session earlier, Office of Management and Budget Director David A. Stockman said the elements of a possible compromise to end the current budget impasse were circulating "below the surface" on Capitol Hill. They could "come to the surface" within two weeks, he said, but he gave no details.

Reagan gave no hint in his address that he was about to soften his stand opposing tax increases or reducing the defense budget buildup.

"From the very beginning, you in the National Association of Manufacturers have supported this administration's program, and when the pressure was turned up a few months ago by those who demand quick fixes and fine tuning, those who got us into the recession in the first place and who now want to deprive working Americans of their tax cuts this July, you kept the faith," Reagan said.

The president thanked the NAM for that, then added, "I also want to ask you to continue your invaluable support."

Reagan said some of the suggestions for change in his program "came from those who were perfectly sincere and troubled, as all of us are, by the projected size of the federal deficit. But some of these suggestions also come from professional insiders who have a vested interest in large bureaucracies and who think they're protecting a political constituency by keeping it helplessly and permanently dependent on government."

Reagan's speech came as White House spokesman David R. Gergen said of the business commmunity yesterday, "Sure, there's been some slippage." But he also claimed that "the business community is very supportive by and large" of the principles of Reagan's economic program even though "there are some questions" about some aspects of it. And Vice President Bush said in a speech yesterday, "I don't know what else this president could do . . . for private enterprise that he hasn't already done."

In his speech, Reagan cited recent sharp declines in inflation--consumer prices rose at only a 3.5 percent annual rate in January and producer prices fell in February--and an increase in personal saving as "encouraging signs" that the economic situation is improving.

A higher savings rate would allow large budget deficits to be financed more easily, he said, noting that the rate, as a percentage of disposable personal income, rose from 4.6 percent in the first quarter of 1981 to 6.1 percent in the fourth quarter.

However, the Commerce Department reported yesterday that the savings rate declined in February for the fourth consecutive month. The February rate was 4.9 percent, down from 5.2 percent in January.