WASHINGTON—The Supreme Court declined Friday to fast-track a decision on whether Donald Trump is immune from prosecution over his efforts as president to overturn his 2020 election loss to Joe Biden.

The high court’s denial of a request from special counsel Jack Smith—announced in a one-sentence order—that it bypass a lower appeals court increases the chances that the former president’s trial on charges that he interfered in the election will be delayed beyond its scheduled March 4 start date. Trump’s lawyers have been seeking to push back the trial, so far without success.