Lt. Gov. Thomas P. O'Neill III, son of the Speaker of the House, announced yesterday he will not seek the nomination to oppose Republican Sen. Edward Brooke and instead would seek reelection to his state post.

O'Neill decision ended what he termed "overwhelming pressure" from Democrats around the nation for him to enter the Senate race. It also took him out of the potentially embarrassing situation of running against Elaine Noble, whom he and his father, Rep. Thomas P. (Tip) O'Neill Jr., have already endorsed.

Noble, the only avowed Lesbian state legislator in the country now appears to be the frontrunner for the Democratic nomination to challenge Brooke, the only black in the Senate.

O'Neill, 33, said the pressure from the Democratic National Committee and state political leaders - who are seeking a stronger candidate than Noble - may now shift to Reps. Michael Harrington or Paul Tsongas, whose recent poll showing Brooke's support slipping set off speculation here that O'Neill would seek the Senate nomination.

Sources here said Tsongas has mentioned a strong possibility of entering the race if O'Neill did not. Neither Tsongas nor Harrington could be reached for comment yesterday.

O'Neill said his friendship for Noble and the public endorsement "was not a central consideration" during the past three days of seclusion with his family to consider running.

"I talked to Elaine out of friendship last week, to tell her I was considering it," he said. "Her reaction was human; she was disappointed. But I said, 'Elaine, I'm just telling you where I am, I wanted you to hear it from me.' I think she appreciated it and we continue to be friends."

Young O'Neill, who heads the Massachusetts state-federal relations office in Washington, said the House Speaker "acted more like a father than a political adviser" this past weekend.

"He said I would make a helluva senator and we'll get you the support and the money you need, but it's you who has to make the decision: you have to walk up that road by yourself and we'll love and respect you for whatever you decide.'

"It may be crazy for me to turn my back on this opportunity, but I really feel the challenge for me right now is in the city and the state," he said. "I asked myself, 'Do I preder Washington to Boston?' and the answer was no. 'Do I prefer the legislature to an executive position?' The answer is no.