WASHINGTON—A battle over Hillary Rodham Clinton’s record as first lady broke out on two fronts Thursday, as a federal judge stepped into a dispute over the handling of still-unreleased Clinton phone logs and Barack Obama’s campaign challenged her record on trade.

The latest twist in the debate over her time in the White House came in the courtroom of U.S. District Judge James Robertson, who forced the National Archives to undergo questioning about why it won’t release 20,000 pages of Clinton’s old phone logs.

Not enough resources, a lawyer representing the National Archives told the judge.

Not a good enough explanation, ruled Robertson, who was appointed to federal court by President Clinton in 1994. Robertson granted a conservative group’s request to question at least one National Archives official on why the agency handles some requests more promptly than others.

The archives deals with requests for documents on UFO sightings while letting the former first lady’s records languish at the former president’s library in Little Rock, Ark., complained Paul Orfanedes, head of the litigation department at Judicial Watch, the organization suing the archives for Clinton documents.

The National Archives wants to delay consideration of the Clinton phone logs for a year, then decide when it will start the six- to eight-month process of reviewing them for possible public disclosure.