The burst of gunfire that injured President Reagan Monday sparked an instantaneous and sharp rise in his popular standing with the American people, according to a new Washington Post-ABC News poll.

The president was already comparatively high in popularity, but his approval rating showed a climb of 11 percentage points from Sunday, the Tuesday, when the news Post-ABC poll was conducted.

While it is common for a president's popularity rating to increase at a time of national crisis, the rise for Reagan appears as sharp as any yet recorded. Reagan's new surge came at a time when the president seemed to be on something of a downward swing in popularity as measured by previous polls.

The new Post-ABC poll was conducted Tuesday night, with 505 people interviewed by telephone nationwide. In the survey, 73 percent of those interviewed said they approve of Reagan's performance as president, 16 percent said they disapprove, and 11 percent expressed no opinion. Because a relatively small number of people were interviewed, the poll has a theoretical margin of error of about 5 percent in either direction.

By chance, The Washington Post and ABC had conducted another nationwide poll last Wednesday through Sunday. In that poll, 62 percent said they approved Reagan's handling of the presidency, 23 percent said they disapproved, and 15 percent offered no opinion. Thus, there was a 7-percentage-point decline after the shooting in the number of people who had a negative opinion of the president.

The gain for Reagan closely resembles the sharp increase in popularity for Jimmy Carter after the taking of American hostages in Iran in November 1979. At that time, according to the Gallup poll, Carter's approval rating jumped from 38 percent to 51 percent almost immediately.

The attempted assassination also served to increase the number of citizens advocating stronger handgun controls, despite a widespread conviction that no law could prevent an assassin from getting a gun and attempting to take the life of a president.

In addition, the Post-ABC poll uncovered evidence of public dissatisfaction with the performance of Secretary of State Alexander M. Haig Jr., whose actions before and after the shooting having made him a center of controversy. Asked whether they approve or disapprove of the way Haig is handling his job, a plurality, 45 percent, said they approve, but 33 percent said they disapprove of Haig and 22 percent expressed no opinion one way or the other.

In contrast to these mixed perceptions of Haig, citizens give a strong endorsement to Vice President Bush. By a margin of 68 percent to 15 percent, those interviewed said they think "Vice President Bush can handle the job of president if he has to."

Political observers predicted immediately after Monday's assault that one result, cold as it may sound, would be to grant the president a so-called second honeymoon with the American public, and thereby blunt potential opposition to his economic recovery program in Congress.

Reagan's economic program has been highly popular with the public despite concern that his call for more than $45 billion in spending cuts would fall most heavily on the poor and that his requested three-year, 30 percent federal income tax decrease would mainly benefit the rich.

In February, shortly after Reagan presented his program in a nationally televised address, a Post-ABC poll showed 72 percent of the public approving the tax cuts.

Since then, scattered opposition from some groups, including the Black Congressional Caucus and Democratic officials, has begun to create a national debate on the Reagan proposals, and public support for them has shown a slight decline. In the polling that ended Sunday, for example, support for both the spending and tax cuts was shown to have dropped by at least 10 percentage points.

Despite rallying to Reagan after the shooting, the public appears to want Congress to conduct a healthy debate on Reagan's proposals, and not to support the president out of sympathy. One question in Tuesday's poll asked whether congressional opponents of Reagan's program should refrain from criticism "until Reagan gets better" or whether members of Congress "should do whatever they think is right about those proposals regardless of Reagan's physical condition."

By a ratio of 2 to 1 -- 61 percent to 32 percent -- the public said Congress should do what it thinks is right about the spending and tax proposals.

On the subject of gun control, the new Post-ABC poll found 65 percent saying they favor "stronger legislation controlling the distribution of handguns," an increase of 8 percentage points from the beginning of March, when the same question was asked by interviewers. A small portion of those favoring stronger handgun control, about 5 percent, said they had opposed such legislation before the attempt on Reagan's life.

At the same time, few people feel that handgun controls would prevent incidents such as Monday's. Seventy-eight percent said they agree that "no gun control law, no matter how strong, could prevent an assassin from getting a gun and shooting a president." Only 18 percent disagreed.

Despite their fear that a president presents a ready target, Americans overwhelmingly reject the idea that presidents should isolate themselves from the citizenry for safety's sake.

Question: "Agree or disagree: From now on the president of the United States should have little or no contact with the public because there is no way to protect him from being assassinated."

The answer: agree, 23 percent; disagree, 72 percent. Nationwide Sample Interviewed by Phone

A random sample of 505 adults nationwide were interviewed by telephone Tuesday on attitudes toward issues arising from the attempted assassination of President Reagan.

Theoretically, figures based on a sample that size are subject to a sampling error of about 5 percent in either direction, 95 percent of the time.

The latest available U.S. Census figures on age, sex, education and race were used to adjust the sample slightly so that it matches the overall population in those characteristics