The department, in a letter sent to the House Judiciary Committee, said the prosecutors would examine allegations that donations to the Clinton Foundation were tied to a 2010 decision by the Obama administration to allow a Russian nuclear agency to buy Uranium One, a company that owned access to uranium in the United States, and other issues.

The letter appeared to be a direct response to Mr. Trump’s statement on Nov. 3, when he said he was disappointed with his beleaguered attorney general, Jeff Sessions, and that longstanding unproven allegations about the Clintons and the Obama administration should be investigated.

Any such investigation would raise questions about the independence of federal investigations under Mr. Trump. Since Watergate, the Justice Department has largely operated independently of political influence on cases related to the president’s opponents…

People close to the White House said there might be another issue at play: Mr. Sessions might be able to forestall the president’s firing him by appointing a special counsel to investigate the uranium deal.