House Majority Leader James C. Wright Jr. (D-Tex.), hoping to quell rumors of dissension in his party's ranks, announced yesterday that most House Democrats have promised to support him when he runs for speaker next year.

Wright said he was making the announcement nearly two years before the vote to "clear the air and dispel rumors and intrigue."

The House has been rife with talk of challenges to Wright and other members of the leadership ever since Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said this would be his last two-year term.

House Democrats will select the new speaker at their December 1986 caucus, provided that they retain control of the House after the 1986 elections.

Wright's announcement yesterday that 184 House Democrats are committed to him appeared to preempt the field and solidify his front-runner's status. However, Democrats cautioned yesterday that a lot can happen in two years.

Wright's list of supporters did not include one major potential challenger, Ways and Means Committee Chairman Dan Rostenkowski (Ill.). Wright said that he had sought Rostenkowski's support and that the Chicago Democrat said he would get back to him.

Listed among Wright's backers was Rep. Richard A. Gephardt (Mo.), chairman of the Democratic Caucus, whom several younger members had urged to challenge Wright. But associates said Gephardt opted not to challenge Wright because he is considering a race for national office, possibly the presidency in 1988.

Wright, a Fort Worth Democrat, is decidedly less liberal than O'Neill, a Boston Irishman who has led the opposition to President Reagan the last four years, and would likely steer a more moderate course than O'Neill has.

Democrats said yesterday that Wright's announcement probably will shift the focus to races for majority leader and majority whip. Only Rep. Thomas S. Foley (D-Wash.), the majority whip, has been campaigning for majority leader.

Several Democrats, including Reps. William V. (Bill) Alexander Jr. (Ark.); Tony Coelho (Calif.), head of the Democratic Congressional Campaign Committee; Charles B. Rangel (N.Y.), and possibly Norman Y. Mineta (Calif.), have expressed interest in becoming majority whip.