Former President Donald J. Trump said on Tuesday that he had received a so-called target letter from the special counsel Jack Smith in connection with the criminal investigation into his efforts to hold onto power after he lost the 2020 election, a sign that he is likely to be indicted in the case.

It would be the second time Mr. Smith has notified Mr. Trump that he is a target in a federal investigation. The first, in June, was in connection to the inquiry into Mr. Trump’s handling of national defense material after he left office and his alleged obstruction of efforts to retrieve it. Mr. Trump was charged with 37 criminal counts covering seven different violations of federal law, alone or in conjunction with one his personal aides.

“Deranged Jack Smith, the prosecutor with Joe Biden’s DOJ, sent a letter (again, it was Sunday night!) stating that I am a TARGET of the January 6th Grand Jury investigation, and giving me a very short 4 days to report to the Grand Jury, which almost always means an Arrest and Indictment,” Mr. Trump posted on his social media platform, Truth Social, after a news inquiry into whether he had been told he is a target.

Two people close to Mr. Trump confirmed that he had received the letter. The former president is expected to decline the invitation to appear before the grand jury.

It is not clear what aspect of Mr. Smith’s investigation into the efforts to obstruct the transfer of power that Mr. Trump’s possible indictment may be related to. The investigation has examined an array of schemes that Mr. Trump and his allies had used to try to stave off defeat, and at least two grand juries have been hearing matters related to his efforts to stay in power.

Mr. Trump’s son-in-law, Jared Kushner, appeared before one of the grand juries in June, according to people familiar with his appearance. Rudolph W. Giuliani, who was Mr. Trump’s personal lawyer, had a recent interview with prosecutors.

Prosecutors have been asking witnesses about the former president’s state of mind, as well as efforts to fund-raise off his false claims of widespread voter fraud and whether he knew he had lost. They have also been scrutinizing efforts to put together slates of so-called fake electors to cast ballots in support of Mr. Trump when the electoral college tallies were certified.

Mr. Trump spent weeks after the 2020 election publicly insisting that he had won and looking for ways to remain in power, at one point considering whether to use the apparatus of government to seize voting machines.

Ultimately, he encouraged a crowd at a rally near the White House on Jan. 6, 2021, to march to the Capitol as Joseph R. Biden’s electoral victory was being certified. Members of the mob stormed the building, some chanting “Hang Mike Pence!” and others hunting for Speaker Nancy Pelosi.