Boosting his claim to a strong southern base, Sen. Albert Gore Jr. (D-Tenn.) has gained pledges of support for his presidential bid from key southern legislators, including a much-coveted endorsement yesterday by Georgia House Speaker Tom Murphy. Murphy brought with him the support of the entire House leadership: 34 committee chairmen and officers.

Gore and Rep. Richard A. Gephardt (D-Mo.) were in a highly contested battle for Murphy's support, with Massachusetts Gov. Michael S. Dukakis a notch behind, after telephoning Murphy five or six times, according to Murphy aide Steve Anthony.

As Murphy explained it, Gore "more closely understands the needs of the region, and they are more accurately reflected in his campaign."

Gore had already secured the backing of legislative leaders throughout the south, including the speakers of the Alabama and South Carolina Houses, majority leaders of the Florida and Kentucky Houses and lieutenant governors of Alabama and Mississippi.

He also has sewed up support from his party's entire political establishment in his home state.

Today, Maryland House Speaker Clayton Mitchell and several state legislators plan to announce support of Gore. Florida House Speaker Jon Mills, former national cochairman of Hart's campaign, and Texas House Speaker Gib Lewis are expected to back Gore next month.

Meanwhile, Sen. Paul Simon (D-Ill.) was endorsed yesterday by 21 New Hampshire Democrats, including the core of the state organization of Sen. Joseph R. Biden Jr. (D-Del.), who dropped out of the race in late September.