According to a new Washington Post-ABC News poll, the Beirut hostage crisis may have produced a marked increase in the number of Americans who are willing to say the United States should distance itself from Israel to minimize the danger of terrorist acts against this country and its citizens.

The nationwide polling, conducted in three stages and ending last Saturday night, found steady increases in the number saying they agree with the statement that "the United States should reduce its ties to Israel in order to lessen the acts of terrorism against us in the Middle East."

In interviews with 508 people on Monday, June 17, 31 percent agreed and 53 percent disagreed with that statement. A poll of another 508 people two days later, on June 19, showed 33 percent agreeing and 53 percent disagreeing. Then in additional interviews with 555 people last Thursday through Saturday, 42 percent said they agreed and 41 percent disagreed.

Because the polling stopped Saturday night, it does not show the effect of Israel's decision to release a first group of 31 Lebanese Moslem prisoners, announced Sunday, or effects of other events of the last three days.

The polling Saturday that showed 42 percent agreeing that the United States should reduce its ties to Israel produced nearly the same result as a poll taken after the massacre of Palestinians at the Sabra and Shatilla refugee camps in Lebanon in 1982. At that time, 42 percent in a national poll said that because of the massacres, for which many held Israel partly responsible, U.S. ties with Israel should be reduced; 47 percent disagreed.

The new poll showed a gradual rise in the feeling that Israel should release more than 700 Lebanese, mostly Shiites, without any request by the United States to do so, if that is what it takes to free the hostages. On June 17, 61 percent took that position; on June 19, 65 percent, and in interviewing Thursday through Saturday, 68 percent.

The public was almost evenly divided on whether the United States should ask Israel to release those Shiites, who were taken captive as Israel moved its troops out of southern Lebanon in recent months. In the last stage of the survey, 42 percent said such a request should be made, and 48 percent said it should not.

Israel's decision to begin releasing its Lebanese prisoners and repeated U.S. and Israeli government statements proclaiming general agreement about how to respond to the hostage-taking may have blunted or reversed the growing public questioning of American-Israeli relations since this poll was completed.

In another crisis, the 1979 U.S. gasoline shortages when motorists had to wait in long lines to fill their tanks, 28 percent in a Washington Post poll said the United States should reduce ties with Israel to ensure an adequate supply of oil from the Arab nations but 48 percent rejected any such action.

The polling Thursday through Saturday also showed a majority of 57 percent holding the view that the United States should negotiate and even give in to terrorist demands if the alternative is further death or injury to hostages. Thirty-six percent said the United States should not negotiate. Those figures show little change from earlier in the week.

In addition, a 53 percent majority at week's end agreed with the statement that "the United States should take military action against any Middle East nation that is found to be aiding terrorist actions against Americans." Thirty-six percent said they disagreed.

President Reagan has maintained a solid approval rating, 62 percent in the Post-ABC News poll, in the days before and after the hostage-taking on June 14. And in polling since June 18, when Reagan held a televised news conference, he has drawn a 69 percent approval rating for his handling of the hostage situation.

Public attention seems riveted on the hostage crisis, and growing. Ninety percent of the people interviewed Thursday through Saturday said they were following events either very closely or fairly closely, up from 80 percent at the outset.