Federal officials and private developers vied yesterday for the right to construct an office complex on a choice, federally owned site east of Union Station to house the administrative headquarters of the federal court system.

The competing proposals, aired at a hearing by the Senate Committee on Environment and Public Works, were offered by three groups: the architect of the Capitol, the nonprofit corporation overseeing the renovation of Union Station and a private development group with other projects in the vicinity.

Chief Justice Warren E. Burger has long urged federal officials to establish an administrative headquarters for court employes and has described the proposed building as "urgently" needed.

Under current plans, the new structure would provide offices for about 700 court employes, who now work at six, widely scattered buildings. It would house the Federal Judicial Center, a research and training agency now spread among three offices. It would also provide space for retired Supreme Court justices.

The 5.5-acre site targeted for the court project is in a rapidly developing area, where new hotels, offices and other ventures are planned. The tract, now occupied mainly by a Senate parking lot, is bounded by First, Second and F streets NE and Massachusetts Avenue.

At yesterday's hearing, Architect of the Capitol George M. White recommended building a federal office structure with an estimated $70.5 million in federal funds. White argued that it "seems appropriate" for the government to own, rather than lease, offices for the court headquarters.

Keith Kelly, executive director-president of the Union Station Redevelopment Corp., which is overseeing the multimillion-dollar restoration of the decaying railroad terminal, countered with a plan to allow his group to develop the site.

Kelly advocated a plan under which developers would be hired by his company to provide commercial offices along with court headquarters on the site. He said his plan would entail no cost to the government and would yield revenue to pay off federal debts for Union Station.

Robert H. Mendelsohn, who heads a Washington development company, responded with a third proposal -- a "partnership" between his firm and the government to build a court office building along with a hotel overlooking Union Station. He said his plan would be the quickest and cheapest for the government.

Mendelsohn's firm is a partner in a group engaged in a $200 million development venture on another nearby site, owned by CSX Corp.

The Reagan administration and Congress are expected to decide soon whether White's, Kelly's or Mendelsohn's plan will prevail.

Under existing law, the Department of Transportation has the right to turn the project over to the Union Station corporation. But Federal Railroad Administrator John Riley said the issue is still under review.

A House committee has endorsed the Capitol architect's plan. But Sen. Robert T. Stafford (R-Vt.), the Senate committee's chairman, described the Union Station option as his "personal preference."