President Reagan today tried to broaden support for his controversial policies in Central America by announcing that a bipartisan commission headed by former secretary of state Henry A. Kissinger would study the "underlying problems" of the region.

In an address to the International Longshoreman's Association in which he praised U.S.-supported guerrillas who are trying to overthrow the leftist Sandinista government of Nicaragua, Reagan again left no doubt that he views the underlying problem as the spread of Marxist movements backed by the Soviet Union and Cuba.

Administration officials said they hoped the announcement would help avert a congressional cutoff of covert U.S. aid to the guerrillas in Nicaragua. The cutoff is to be debated Tuesday in a secret session of the House with an open vote to follow.

The officials said they also hoped the new group, to be called the National Bipartisan Commission on Central America, could be used to prod Congress to increase military aid to the U.S.-supported government of nearby El Salvador in its civil war against leftist rebels.

Reagan did not announce the name of any commission member except Kissinger, to whom the president referred as "virtually a legend" in diplomacy. But administration officials, some of whom met during the day to discuss the composition of the commission, said most of the other members also had been picked.

Among Democrats who have agreed to serve, according to the officials, are former Democratic national chairman Robert S. Strauss, AFL-CIO President Lane Kirkland and Yale economics Prof. Carlos Diaz Alejandro. The Republicans were said to include Bill Clements, former governor of Texas, and Nicholas Brady, an investment banker and former senator from New Jersey.

Cardinal Terence Cooke of New York and William Walsh of Project Hope also have agreed to serve, according to the officials, and John S. Silber, president of Boston University, is expected to be a member. The officials said two or three more people may be added to the group.

Administration officials said that Kissinger, who met with senior officials in the White House late last week, at first rejected being named chairman of the commission, though he was willing to be a member. His resistance was based on the time he would be required to spend away from his foreign affairs consulting business, these officials said.

But after further discussions Kissinger agreed to take the post, and Reagan called him Sunday evening to offer the chairmanship.

A senior administration official acknowledged that Kissinger, former secretary of state and national security affairs adviser to Presidents Nixon and Ford, was controversial with both liberals and conservatives. But the official said Kissinger's recommendations would carry weight with the State Department and his appointment would give Central America policy high visibility.

"He's a dynamic figure," this official said. "The entire national security community feels that Kissinger is better equipped to report on both a medium- and long-range solution than anyone else. Also, he wasn't heavily involved in Central American policy in the past, so his appointment doesn't raise old concerns."

Kissinger's name was greeted by silence when Reagan announced it today to the convention of union delegates. The longshoremen, who applauded the president politely when he entered and departed and when he referred to the union and its president, Thomas W. Gleason Sr., sat silently throughout his denunciation of communism in Central America except for one moment of mild applause.

The administration's "senior counselor" on the new commission will be U.N. Ambassador Jeane J. Kirkpatrick, who has taken a leading role in forming U.S. policy in Latin America. In addition, there will be eight congressional counselors, four from each house, divided between Democrats and Republicans.

Democratic counselors from the Senate will be Henry M. Jackson (D-Wash.), one of the principal sponsors of congressional proposals for such a commission, and Lloyd Bentsen (D-Tex.). Sen. Charles McC. Mathias Jr. (R-Md.) and Rep. Jack Kemp (R-N.Y.), who are also among sponsors of the proposal, are expected to be two of the Republican counselors.

According to a White House official who briefed reporters on Air Force One traveling from Andrews Air Force Base to Florida today, the commission will report to Reagan by Dec. 1 after studying "the nature of U.S. interests in Central America and the threats now posed to those interests."

"They will be asked to give advice to the president on a long-term U.S. policy that will respond to the challenges of social, economic and democratic development in the region and to threats to instability and security," the official said.

The Reagan administration turned to bipartisan commissions to resolve difficult political problems on Social Security and the MX missile. Reagan's action today came against a backdrop of escalating war in Central America, where the CIA is planning to support a rapidly growing "secret army" of 12,000 to 15,000 anti-Sandinista rebels in Nicaragua, according to official sources.

Reagan has become increasingly open in expressing support for these rebels, whose representatives have briefed administration officials in the White House and the adjoining Executive Office Building. Today, Reagan made clear that he supports not only the government in El Salvador against leftist rebels there but also the anti-Sandinista guerrillas in Nicaragua.

"Nicaragua is today a nation abusing its own people and its neighbors," Reagan said. "The guerrilla bands fighting in Nicaragua are trying to restore the true revolution and keep the promises made to the OAS Organization of American States . Isn't it time that all of us in the Americas worked together to hold Nicaragua accountable for the promises made and broken four years ago?"

In his speech today Reagan used biting anti-communist rhetoric, most of it greeted silently by a union known for its anti-communism, and blamed the Soviets and the Cubans for most of the trouble in the region.

"There is a war in Central America that is being fueled by the Soviets and the Cubans," Reagan said. "They are arming, training, supplying and encouraging a war to subjugate another nation to communism--that nation is El Salvador. The Soviets and the Cubans are operating from a base called Nicaragua. And this is the first real communist aggression on the American mainland."

Reagan praised members of Congress of both parties for proposing the bipartisan commission on Central America. But he warned that military assistance for El Salvador could not be put on the congressional back burner while the commission studies a wide range of proposals, probably including massive economic aid similar to the Marshall Plan that reconstructed Europe after World War II.

While the commission is engaged in its study, Reagan, said, "we must not allow totalitarian communism to win by default."

The 116,000-member Longshoremen's union Reagan addressed today was one of the few to endorse him in the 1980 presidential campaign. Other presidents have shied from the ILA, which has seen more than 30 officials, including 10 vice presidents, convicted of racketeering, extortion and similar charges since 1977.

FBI Director William H. Webster has been critical of corruption in the union. White House spokesman Larry Speakes last week declined to respond to questions from reporters when asked about Webster's criticism of the ILA.

Reagan praised Gleason, an opponent of the administration's anti-racketeering legislation who has said he invoked the Fifth Amendment and refused to answer questions of a federal grand jury investigating charges of ILA corruption. Reagan said Gleason demonstrated "the kind of integrity and loyalty that's hard to come by today."

The president was flanked by Gleason and Secretary of Labor Raymond J. Donovan as he spoke. Also at the head table was Kemp, who accompanied Reagan when Gleason made his presidential endorsement on a windswept Buffalo pier in 1980.

Reagan made several verbal stumbles during his speech, apparently because he was bothered by reflections on the teleprompters. Except for mentions of Gleason's name, his audience showed little enthusiasm.

In his remarks, the president said approvingly that "ILA" meant "I Love America," the slogan which also appeared on a banner on the wall of the Diplomat Hotel, where the union is holding its convention.

"With a timely investment now, we can save freedom in Central America," Reagan said in concluding. "And I believe we must make that investment. I believe we have a moral responsibility to do so. And I believe with the help of organizations like the ILA we will succeed in expanding freedom for the people of Central America."