The former director of the FBI that led the investigation into President Trump’s ties to Russia during the 2016 presidential campaign, James Comey, says prosecutors are probably under “intense pressure” to decide whether to charge Mr. Trump before he officially becomes the Republican nominee for 2024.

In an interview with President Biden’s former press secretary, Jen Psaki, that aired on MSNBC Sunday, Mr. Comey — whom Mr. Trump fired in 2017 — speculated that special counsel Jack Smith’s case involving classified documents sequestered by Mr. Trump at his Mar-a-Lago estate in Florida could be the strongest of several now looming over the former president. That the drama is being played out so close to a presidential election makes Mr. Smith’s job all-the-more difficult, he said.

“We desperately don’t want to be involved in election-time investigations and near them, so they are feeling something else that won’t be talked about publicly,” Mr. Comey said. “I just know the system — they’re feeling intense pressure to move, to move, to move, so they’re not in the position of making a charging decision next year when Donald Trump may be the nominee.”

“I think they are likely working very, very hard in trying to get ahead of even the normal pace of what an investigation might be,” he added.

Mr. Comey’s remarks come just as a federal grand jury hearing evidence on the classified documents case is set to return to its deliberations this week following a lull of several weeks. Late Saturday, NBC News, citing unnamed sources close to the investigation, reported the development but said there is no word yet as to whether prosecutors will seek an indictment of Mr. Trump in the case.

Mr. Comey suggested that last week’s disclosure that Mr. Smith and his team have audio recordings of the president lamenting that he could not share the details of documents purportedly related to an American attack on Iran to visitors at his Bedminster, New Jersey because they were classified could be a powerful tool for the prosecutor. The comments would appear to undercut Mr. Trump’s assertions that he had declassified all the documents he removed from the White House.

“Tapes are amazing for a prosecutor because you can’t cross-examine a tape, you can’t call a tape a liar, a deep-state operative,” Mr. Comey told Ms. Psaki. “A tape is you saying what you think, which is why they’re so valuable in an organized-crime case, and they’ll be so valuable and important to Jack Smith in this documents case.”

Mr. Comey added that any prosecutor would be concerned that a high-profile case such as the one being handled by Mr. Smith is playing out during a presidential primary.

“I mean it’s this crazy world that Donald Trump has dragged this country into, but he could be wearing an ankle bracelet while accepting the nomination at the Republican Convention,” he said. “It looks like the Republicans will likely nominate someone who is under serious criminal investigation or he’s indicted, and who knows where that’s going to lead us.”

Mr. Comey, a longtime Republican who switched parties to vote for President Biden over Mr. Trump in 2020, said he would support the incumbent again next year. He called the prospect of another Trump term “four years of a retribution presidency.

“He could order the prosecution of individuals who he sees as enemies. I’m sure I’m on the enemies list,” Mr. Comey said. “Our Constitution really does give a rogue president — which is what this would be — tremendous power to destroy.”