White House spokesman Larry Speakes said yesterday that reporters have been spreading false rumors that the White House pressured the space agency to launch the shuttle Challenger Jan. 28 to coincide with President Reagan's scheduled State of the Union address.

"It is the most vicious and distorted rumor I have ever heard," Speakes said at a White House briefing. "I'm tired of that story; I'm really tired of it. I bet not a soul in here has gotten that from an official source. You've gotten it from your friends . . . . It is a rumor perpetrated by the press."

Speakes said he had received a number of inquiries from reporters suggesting that White House officials had urged the National Aeronautics and Space Administration to launch the shuttle that day so it would fit with the speech Reagan was to deliver that night. After the shuttle exploded, killing its seven crew members, the president postponed his address for a week.

The speech, as it was written for delivery on the 28th, included a reference to the manned space station and to an experiment on the shuttle by a young man who was to be saluted as a "hero" by the president, Speakes said.

He challenged reporters to produce any official source for the rumors. One version, Speakes said, had White House chief of staff Donald T. Regan telling NASA officials to "get that thing up."

"Absolutely not," Speakes said yesterday. Asked whether there was any talk of using a "split screen" to broadcast the shuttle crew while Reagan was making his speech, Speakes said that was "more of the vicious rumor. You really ought to get off it."

Speakes' comments echoed remarks top White House officials have made to reporters asking if there was a connection between the president's address and the shuttle launch. Engineers at Morton Thiokol Inc., which manufactures solid rocket boosters for the shuttle program, have accused NASA of pressuring them to approve a Jan. 28 launch of Challenger despite unusually cold weather in Florida, but White House officials have repeatedly denied pushing the space agency.

"We didn't tell them to fly the shuttle. If you're talking about pressure to launch on that day, no, absolutely not. No pressure, period," Speakes said.

He added that he appreciates reporters' "responsibility in coming to us promptly with rumors, which we knocked down immediately."