WASHINGTON — The Supreme Court on Monday agreed to review two major Trump administration immigration initiatives: a program that has forced at least 60,000 asylum seekers to wait in Mexico while their requests are heard and the diversion of $2.5 billion in Pentagon money to build a barrier on the southwestern border.

Lower courts blocked both measures.But the Supreme Court, in earlier orders, allowed them to remain in effect while appeals moved forward.

The arguments in the two cases will not be heard until after the November election. Should President Trump’s Democratic opponent, Joseph R. Biden Jr., win, his administration could take steps to make the cases moot.

In the case on asylum seekers, an appeals court in February blocked the program, known as Remain in Mexico, saying it was at odds with both federal law and international treaties and was causing “extreme and irreversible harm.”