President Reagan said yesterday that U.S. support for the rebels fighting Nicaragua's government is "morally right and intimately linked to our own security."

Reagan said that failure to support the rebels would "send an unmistakable signal that the greatest power in the world is unwilling and incapable of stopping communist aggression in our own backyard."

"If we refuse to help their just cause, if we pull the plug and allow the freedom fighters to be wiped out by the same helicopter gunships the Soviets are using to murder thousands of Afghans, then our ultimate price to protect peace, freedom and our way of life will be dear indeed," Reagan said in his weekly radio address, delivered from the presidential retreat at Camp David.

Reagan next month is expected to request that Congress release $14 million in aid for the Nicaraguan "contras," despite strong opposition on Capitol Hill to such assistance.

Rep. William V. (Bill) Alexander Jr. (D-Ark.), in the Democratic response to Reagan's address, accused the president of "supporting guerrilla groups intent on the violent overthrow" of Nicaragua's Sandinista government.

"Mr. Reagan's alliance with violence in Nicaragua is against the American way," Alexander said. "It is contrary to the principles of our Founding Fathers. The real enemies in Central America are poverty, ignorance, hunger, social injustice and political corruption."

Reagan said the "price" of refusing to provide the aid could be the bringing of "tyranny to our own borders, carrying the same specter of economic chaos, the same threat of political terrorism, the same flood tides of refugees we've seen follow every communist takeover from Eastern Europe to Afghanistan, Laos, Vietnam, Cambodia, Ethiopia and now Central America."

Reagan said Cuba and Nicaragua have been caught trying to spread communism. He added that a failure by the rebels would make it "much easier" for the Soviet Union to "intimidate other nations and to expand their empire."

"I know many well-intentioned people would rather not accept these facts," Reagan said. "But we have -- we, who have the responsibility for governing cannot afford to be ostriches with our heads in the sand."