President Reagan vowed today that terrorists "will never succeed in weakening our resolve" but said the United States would "continue to act with appropriate restraint" in response to the Beirut hostage crisis.

Reagan's comments followed an emotional private meeting at Reunion Arena here with family members of three of the hostages. The president offered reassurances that he is doing "all in our power" to win release of the Americans, aides reported afterward.

"He told them that our paramount interest is the safety of those being held, and that we were making diplomatic efforts to try and gain their release," White House spokesman Larry Speakes said.

"The families were very supportive of the way the president is approaching the matter," he added.

National security affairs adviser Robert C. McFarlane remained behind to talk further with the families after their 15 to 20 minutes with Reagan.

The president, sitting in a folding chair, met with the family of Allyn Conwell, originally from Houston, who was selected as a spokesman for the Trans World Airlines Flight 87 hostages at a news conference in Beirut Thursday.

Reagan met at the same time with the families of hostages Vicente Garza and his son-in-law, Robert Trautmann Jr.

Family members embraced Reagan today with tears in their eyes, Speakes said.

The president skipped a session with a tax-reform group to meet with the families.

Speakes said they did not urge swapping the American hostages for more than 700 Israeli-held Lebanese prisoners, most of them Shiite Moslems, whose release the hijackers are demanding. Asked if any concern was expressed by the families about a lack of Israeli cooperation, Speakes said, "I just don't want to get into that."

Reagan devoted most of his subsequent address before the Lions Club International convention to tax reform, but added brief remarks on the hostage situation and other recent terrorist acts.

"In the last few days," he said, "it has become even more clear that the criminal threat to civilization is no mere domestic problem."

He then referred to this week's shootings in El Salvador, in which 13 people died, including six Americans, four of whom were Marines; the bombing in Frankfurt, West Germany; the hijacking of Flight 847, and last week's seizure of a Jordanian aircraft.

"The killers in El Salvador are no different than those other perpetrators of inhumane acts," he said. "I can promise all of them this: they will never succeed in weakening our resolve to resist terrorism."

The audience of nearly 20,000 applauded strongly.

"We will continue to act with appropriate restraint," Reagan said. "But let no one doubt our resolve. Those who commit such crimes should be aware of the truth of President Theodore Roosevelt's observation. 'The American people,' he said, 'are slow to wrath, but once their wrath is kindled, it burns like a consuming flame.' "

This drew even stronger applause, and Reagan left to a standing ovation.

Reagan went to Camp David late this afternoon and is to fly Saturday afternoon to Andrews Air Force Base for a ceremony marking the return of the bodies of the four Marines killed in San Salvador.

En route from Texas back to Washington today, Reagan spoke by telephone with Salvadoran President Jose Napoleon Duarte, who offered condolences, Speakes said.

He said Reagan pressed Duarte to activate a unit trained about a year ago to probe incidents such as Wednesday's.

Concerning Lebanon, Speakes told reporters that the United States has not informed other governments that Israel will release its Shiite Moslem prisoners if the hostages in Beirut are freed. Although it is "our judgment" that this would happen, Speakes said, "the only thing we're contacting other governments on is if they can bring influence" on Nabih Berri, leader of the Amal movement, who has agreed to negotiate on behalf of the hijackers.