Sen. Robert C. Byrd moved closer to another term as the Senate's Democratic leader yesterday when he announced that he and the two other top Democratic leaders would seek reelection to their posts as "a team" at the start of the 100th Congress next January.

The announcement removed Sen. Daniel K. Inouye (Hawaii), the secretary of Democratic Conference, as a potential challenger to Byrd as the party's Senate leader, a post Byrd (W.Va.) has held since 1977. However, Byrd's path to another term was not entirely clear because of what Democratic aides described as an active campaign for the leadership post being waged by Sen. J. Bennett Johnston (La.).

Johnston confirmed last night that he is seeking the Democratic leadership post. Earlier yesterday, he met with Byrd, Inouye and Democratic Whip Alan Cranston (Calif.) to tell them of his plans, apparently prompting the three current leaders to announce for reelection.

"I think it's going very well," Johnston said of his efforts to line up support, adding that he has talked to every Senate Democrat. "I think I can win," he said.

Johnston's efforts among other Democratic senators intensified over the past week, which one party source confirmed was a key factor in prompting Byrd to announce the reelection plans of the current leadership team in an attempt to head him off.

The aide said Byrd, who was described as having worked to line up votes for a year, feared Johnston may soon publicly announce a challenge, and that continuing rumors about a possible contest for the leadership post may hurt Democratic election chances in the fall.

The early announcement was partially intended to defuse Johnston's campaign and discourage any other potential challengers to Byrd, the aide said.

Byrd, Inouye and Cranston have scheduled a news conference today to explain the decision to seek reelection to their current positions.

Henry Giugni, Inouye's administrative assistant, said Inouye "just felt it best to go along with Byrd to help the Democrats regain their majority" in the Senate. He said Inouye had promised Byrd "a long time ago" that he would support him for another two-year term as Democratic leader.

Inouye was considered a potentially strong challenger to Byrd for the leadership post, which would take on added importance if the Democrats regain control of the Senate in this year's congressional elections. The Republicans currently hold a 53-to-47 majority in the Senate, where Byrd is the minority leader.

In addition to Inouye, Democratic aides said that Sen. Lawton Chiles (Fla.), who unsuccessfully challenged Byrd for the leadership post last year, has also decided not to run again for the job.

Chiles mounted his challenge last year after Byrd had already locked up near-majority support. Although Chiles finished a distant second, it marked the first time that Byrd had faced any party challenger since he assumed the leadership post, reflecting a restiveness in Democratic ranks over his style of leadership.

Byrd is considered a master of Senate internal politics and procedures, but has been criticized by some as a lackluster public spokesman for the party. This criticism has intensified since the Democrats lost their Senate majority in President Reagan's landslide 1980 election.

Johnston said he has been telling his colleagues that while Democrats enjoy a "natural advantage" on issues and personalities, they must use "imagination" and "anticipate rather than react" to succeed in countering Republican gains under Reagan.