WASHINGTON — The entire federal appeals court in Washington said on Friday that it would take up two cases that raised the question of whether and when Congress may sue to resolve a dispute with the president, setting up a double-barreled test for establishing when the judicial branch can resolve disputes over separation of powers.

In a terse order, the full appeals court said it would rehear a case involving a House Judiciary Committee subpoena to Donald F. McGahn II, President Trump’s former White House counsel, vacating a 2-1 panel ruling last month that Congress could not sue to enforce its subpoenas of executive branch officials.

The full court also said it would immediately take up a case that House Democrats brought against Treasury Secretary Steven Mnuchin challenging the administration’s use of emergency powers and other extraordinary measures to spend more taxpayer funds on Mr. Trump’s border wall with Mexico than Congress had been willing to appropriate.

In the border wall case, a United States District Court judge had sided with Mr. Trump and dismissed the case, saying the House had no standing to bring it. An appeals court panel heard arguments in the case weeks ago but has not yet issued a ruling. The order said that the panel had requested that the full court hear that case since it also raised an issue of standing.