WASHINGTON (AP) _ More than 250 House members, determined to keep closer tabs on NASA after the Challenger accident, are called on the space agency today to hold a "full, fair and open competition" to find a second source for the shuttle's booster rockets.

''Now is the time, particularly as the agency moves to redesign the solid rocket motors, to begin the qualification process for an additional contractor,'' the lawmakers said in one of two letters written to James C. Fletcher, administrator of the National Aeronautics and Space Administration.

At a news conference in the Capitol, several House members said development of an additional source for the booster rockets could cut costs by as much as $10 million with each shuttle flight, even though it might cost NASA a minimum of $40 million to $50 million in initial testing costs.

NASA's estimates of the testing costs runs as high as $80 million to $100 million, which it says is not available in a time of budget austerity and when, sources say, the administration trying to find savings of more than $2 billion to pay for a replacement for the shuttle Challenger.

Rep. Robert Torricelli, D-N.J., said the second-source proposal was "good for costs, good for safety, good for quality" of the space program.

Torricelli was joined by Reps. Bill Lowery, R-Calif; Vic Fazio, D-Calif. and Mel Levine, D-Calif., at the news conference.

Their effort to gather signatures among House members has been aided by Hercules, Inc., a firm that hopes to win a government contract to make some rockets in the future.

The congressmen said that if NASA failed to agree with their suggestion they would try to impose it through legislation. "NASA needs to understand that we are in a new relationship and the Congress is going to expect better and faster results when we make suggestions," Torricelli said.

The letter drafted over Lowery's signature calls for a "full, fair and open competition" to develop a second source for booster rockets, and cites the spaceagency's own statement that such a development would be in the national interest.

Currently, NASA has a contract with Morton Thiokol Inc. to produce all shuttle booster rockets. A presidential investigating commission is going to lay the blame for the Jan. 28 explosion of the Challenger on a faulty seam in the Challenger's right booster rocket.

Any competing company that wins a contract would be required to manufacture the same rocket as Morton Thiokol, but many lawmakers believe competition would save money as well as give the space program a hedge against any single company's difficulties.

Word of the letters circulated well in advance of the news conference, and NASA congressional relations chief John F. Murphy said his agency has ''no objections to the concept of a second source. It's only a money problem.''

He said NASA does not have the money to pay for the kinds of tests a second company would have to run to produce a rocket qualified for flight.

The letters are the freshest indication of a tougher attitude in Congress toward NASA in the wake of the nation's worst space disaster. Until Jan. 28, congressional criticism of the space agency was rare and the praise generous. But since the loss of the Challenger, lawmakers have expressed deep concern for revelations about the agency's management practices, and vowed to take a closer look at NASA in the future.

At the same time, the support that has developed for the letters was partially the result of a bid by several companies, including Hercules Inc., to cut into Morton Thiokol's booster rocket monopoly.

Several congressional sources, who asked not to be identified by name, said Hercules official Ann Minor had telephoned their offices seeking signatures on the letters, and she confirmed her role.

The lawmakers called their news conference as the investigative commission prepared to present its report to President Reagan on Monday. Commission Chairman William P. Rogers met Wednesday with relatives of the seven crew members killed in the accident.

The families did not discuss their briefing, and issued a statement beforehand saying they would not respond to questions from reporters.

The accident also produced new repercussions within NASA itself, with an announcement of early retirement by William R. Lucas, the longtime director of the facility that supervises the booster rockets.

Lucas, 64, made his announcement in a closed circuit television speech to employees at the Marshall Space Flight Center in Huntsville, Ala. ''Now that the causes of the accident are well enough understood so that the problem can be fixed, and because corrective action already has begun, and inasmuch as the space shuttle cannot fly again before the end of 1986, I have concluded that it is appropriate for me to retire now and allow my successor to become firmly established,'' he said.