WASHINGTON—A divided Supreme Court on Wednesday declined to suspend a lower court’s order that directed the Trump administration to resume nearly $2 billion in foreign-aid funding.

Last week, Chief Justice John Roberts briefly paused a deadline for the government to make the payments. The order Wednesday, which came on a 5-4 vote, removed that hold. The court’s majority, however, instructed a federal trial judge to give “due regard for the feasibility of any compliance timelines.”

Four dissenters, led by Justice Samuel Alito, said recipients of foreign-aid funding had raised serious concerns about the government not paying them for work they had completed. But the trial judge, they said, was “too extreme” in ordering the payments to be made within 36 hours.

During its first few weeks, the Trump administration largely dismantled the work of the 10,000-person U.S. Agency for International Development and the thousands of people in nonprofits and other groups that work with it. Its headquarters were closed and most of its staff was put on paid leave, and those around the world were ordered to come home within a month.

Several lawsuits have challenged the administration’s actions.

Write to Mariah Timms at mariah.timms@wsj.com