By nearly 2 to 1, the American people support the vote in the House last week to deny $100 million in military and nonlethal aid to the Nicaraguan rebels, according to a new Washington Post-ABC News public opinion poll.

In addition, a majority of those polled disapproved of President Reagan's handling of the situation in Nicaragua, a setback for the president who had for months been receiving extremely high ratings for his conduct of foreign affairs.

The poll began Thursday evening, shortly after the House voted 222 to 210 to turn down Reagan's request for aid to the counterrevolutionaries, or contras. Interviews with 1,147 people through Monday night showed 60 percent approving of the House vote, 35 percent disapproving, and 5 percent offering no opinion.

On the question of Reagan's handling of the situation in Nicaragua, 52 percent said they disapproved, 37 percent approved, and 11 percent expressed no opinion.

The new survey showed a striking increase in public awareness of events in Nicaragua, with 59 percent able to state that it was the contras, not the Sandinistas, that the Reagan administration was supporting.

In five previous Post-ABC News polls from 1983 to 1985, the number able to identify which side the United States was backing ranged from a low of 25 percent to a high of 37 percent. In two of those surveys, plural- ities thought the United States was supporting the Sandinis- tas.

In recent weeks, Reagan has focused attention on Nicaragua almost every day in an attempt to persuade the nation that the Sandinistas are a threat to U.S. national security. He has asked the public to apply pressure on Congress to vote for aid to the contras.

The new poll, however, shows the public basically sticking to views it has held for years. Thirty-two percent said they regard Nicaragua as a major threat to U.S. security, 24 percent said it is a minor threat, 37 percent said it is not a threat at all, and 7 percent offered no opinion.

In January 1984, the last time the Post-ABC News poll made such an inquiry, 28 percent said Nicaragua was a major threat, 25 percent saw it as a minor threat, 32 percent as not a threat at all, and 15 percent had no opinion. The main difference between then and now appears to be that some of the "no-opinions" have moved either toward the Reagan position or away from it.

Asked whether "the United States should be involved in trying to overthrow the government in Nicaragua or not," 28 percent in the new survey said yes, 62 percent no, and 10 percent offered no opinion.

While lopsided on the side of nonintervention, those figures do show the Reagan view making some inroads since the last time the Post-ABC News poll asked that question. At that time, in March 1985, 16 percent supported U.S. involvement in overthrowing the Sandinistas and 72 percent were opposed.

The most support for U.S. involvement in overthrowing the Sandinistas was measured at 30 percent, in a Post-ABC News poll taken shortly after the invasion of Grenada in 1983.