Public support for President Reagan's handling of the hijacking of Trans World Airlines Flight 847 increased sharply after his televised news conference Tuesday, according to a Washington Post-ABC News nationwide public opinion poll.

On Monday, 48 percent of those interviewed said they approved of Reagan's handling of events after the hijacking by Lebanese Shiite terrorists last Friday. On Wednesday, the day after the news conference, 68 percent said they approved.

There also was a substantial increase in support for Reagan's refusal to negotiate with the terrorists, according to the poll.

A majority in the survey said they would rather see the United States negotiate and even give in to the terrorists' demands, if the alternative is injury or further loss of life to the 40 American men still being held. But that majority was considerably smaller after Reagan's nationally televised news conference than before it.

The percentage of respondents who said the government of Israel is not doing as much as it should to help resolve the crisis also increased after the news conference. On Monday, 49 percent of the people interviewed said Israel is not doing enough. On Wednesday, that figure was 58 percent.

Despite growing overall support for Reagan's handling of the situation, there are sharp divisions in attitudes between men and women, blacks and whites and Republicans and Democrats.

One of the key questions asked people which of two courses they prefer: "The United States should be negotiating for the release of the hostages, even if that means giving in to the terrorists' demands; or "The United States should not be negotiating, even if some of the Americans taken hostage are injured or killed."

In interviewing Monday, 59 percent favored negotiating and 32 percent were opposed -- a gap of 27 percentage points. On Wednesday, 53 percent were for negotiating and 40 percent were opposed -- a gap of 13 points.

Some of the sharpest divisions came in response to that question. Among men, half favored negotiating, even if that means giving in to the terrorists, and half were opposed. But among women, 65 percent favored negotiating and 26 percent were opposed.

Republicans were evenly divided, but Democrats favored negotiating by more than 2 to 1.

Another survey question found 61 percent of men supporting military action against any Middle East nation that is found to be aiding terrorists who prey on Americans, and 35 percent of them opposing such action. But women were almost evenly divided, 44 percent in favor, 42 percent opposed.

The terrorists' chief demand is that Israel release more than 700 Lebanese Shiite prisoners taken as Israeli troops withdrew from southern Lebanon in recent months.

In the poll, 41 percent said the United States should ask Israel to free those prisoners, and 49 percent said no such request should be made. There was little change in sentiment from Monday to Wednesday.

Asked whether they agreed with the statement that "the U.S. should reduce its ties to Israel in order to lessen the acts of terrorism against us in the Middle East," 32 percent agreed, 53 percent disagreed, and 15 percent offered no opinion.

Among blacks there was an almost even split on that question: 44 percent said ties should be reduced, 46 percent said they should not be. About 100 blacks were interviewed in the random survey, making the figures for blacks as a group substantially less reliable than those for whites.