Rep. Chris Van Hollen (D-Md.) has scored the first union endorsement in the race to replace Sen. Barbara A. Mikulski (D-Md.), winning support from a Maryland branch of the International Brotherhood of Teamsters.

The Baltimore-based union represents about 10,000 families in the state. The endorsement came the same day Van Hollen announced his opposition to a bill that would ease passage of a major free trade agreement, something labor unions oppose.

His primary rival, Rep. Donna Edwards, meanwhile, is touting new allies in her own backyard of Prince George’s County. Seven of the nine members of the county council will endorse her campaign on Wednesday.

National unions have yet to weigh in on the primary between Van Hollen and Edwards, who was backed by several labor heavyweights when she unseated incumbent Democratic Rep. Albert Wynn in 2008. The field is also unsettled — Rep. Elijah Cummings and former lieutenant governor Kathleen Kennedy Townsend are among the potential candidates still looking at the race.

But the two declared candidates are already locked in a fierce competition for local and national support.

Van Hollen has secured more backers inside the state, including Prince George’s County Executive Rushern L. Baker III. Edwards has support from more national groups, including the powerful feminist organization Emily’s List.

On Monday, Edwards announced that Carol Moseley Braun, the first African-American woman to serve in the Senate, had endorsed her campaign. Van Hollen on the same day rolled out an endorsement from former labor secretary Robert Reich.