Assistant Secretary of State Elliott Abrams vowed yesterday to stay in his job and said the Iran-contra hearings may build support for the Reagan administration's policies in Central America.

Abrams said he is "delighted with the support" he is being given by Secretary of State George P. Shultz and President Reagan.

Abrams' vow came as 129 House Democrats sent a letter urging that he be sacked. The letter to Shultz said Abrams had deceived Congress about his role in the Iran-contra scandal and can no longer serve effectively.

"He must resign or be replaced immediately," it said.

Abrams, who has been under fire for making false and misleading statements to Congress, was asked by reporters whether he intends to stay at his post overseeing U.S. policy in Latin America.

"Absolutely," he replied. "I have no plans to go anywhere."

Shultz has said Abrams is doing a "sensational job." Reagan, at a news conference in Venice Thursday, merely cited Shultz's comments when asked about Abrams.

Abrams' comments yesterday followed a speech to a conservative group, Citizens For America. He discussed the administration's military support for the contras fighting Nicaragua's Sandinista government.

He received a standing ovation and did not mention the controversy swirling around his job performance.