Some of the questions posed during the arguments probed hypothetical examples of presidential wrongdoing such as selling nuclear secrets, ordering a coup or political assassination or taking a bribe.
But some of the conservative justices, who hold a 6-3 majority, voiced concern about presidents lacking any level of immunity including for less obviously egregious acts.
"We're writing a rule for the ages," conservative Justice Neil Gorsuch said during the arguments.
Trump appealed after lower courts rejected his request to be shielded from four election-related criminal charges on the grounds that he was serving as president when he took the actions that led to the indictment obtained by Special Counsel Jack Smith.
Conservative Justice Samuel Alito said a president is in "a peculiarly precarious position" as he expressed concern about presidents having to worry about being indicted.
Donald Trump has not attended the Supreme Court because he is in a Manhattan courtroom. (EPA PHOTO)
"If an incumbent who loses a very close, hotly contested election knows that a real possibility after leaving office is not that the president is going to be able to go off into a peaceful retirement but that the president may be criminally prosecuted by a bitter political opponent - will that not lead us into a cycle that destabilises the functioning of our country as a democracy?" Alito asked Michael Dreeben, the lawyer representing the special counsel.
"And we can look around the world and find countries where we have seen this process where the loser gets thrown in jail," Alito added.
"So I think it's exactly the opposite, Justice Alito," Dreeben responded.
"There are lawful mechanisms to contest the results in an election."
D John Sauer, the lawyer arguing for Trump, painted a dire picture of the presidency without immunity.
"Without presidential immunity from criminal prosecution, there can be no presidency as we know it. For 234 years of American history, no president was ever prosecuted for his official acts," Sauer told the justices.
"If a president can be charged, put on trial and imprisoned for his most controversial decisions as soon as he leaves office, that looming threat will distort the president's decision making precisely when bold and fearless action is most needed," Sauer added.
Dreeben told the justices that the Supreme Court has never recognised the kind of immunity that Trump seeks for a public official.
Conservative Chief Justice John Roberts signalled concern about relying merely on the "good faith" of the prosecutors to prevent abusive prosecutions against presidents if the Supreme Court rejects presidential immunity.
"I do think that there are layered safeguards that the court can take into account that will ameliorate concerns about unduly chilling presidential conduct," Dreeben responded.
"That concerns us. We are not endorsing a regime that we think would expose former presidents to criminal prosecution in bad faith, for political animus, without adequate evidence. A politically driven prosecution would violate the constitution."
Conservative Justice Clarence Thomas asked Dreeben why no president had been prosecuted before now, citing a controversial Cold War-era US operation in Cuba.
"The reason why there have not been prior criminal prosecution is that there were not crimes," Dreeben responded.
Alito asked Dreeben whether president Franklin Roosevelt's decision to intern Japanese Americans during World War II could have brought criminal charges as conspiracy against civil rights.
"Today, yes," Dreeben said, given a more recent Supreme Court precedent.
Progressive Justice Elena Kagan pressed Sauer on hypothetic scenarios to get his response on whether they would be an official act that would be immune from prosecution under Trump's claim.
"If a president sells nuclear secrets to a foreign adversary, was that immune?" Kagan asked.
Sauer responded that if it is "structured as an official act" the president could not be prosecuted unless he is first impeached and removed from office by Congress.
"How about if the president orders the military to stage a coup?" Kagan asked Sauer.
"That may well be an official act," Sauer responded, meaning no prosecution without impeachment and removal first.
Trump has pleaded not guilty in this case and in three other criminal cases he faces, including an ongoing trial on New York state charges related to hush money paid to a porn star shortly before the 2016 US election.
Trump did not attend the Supreme Court arguments because he was in a Manhattan courtroom in that case.
Sauer raised three hypothetical examples of past presidents being charged for officials actions taken as president.
He asked whether George W Bush could be prosecuted for obstructing an official proceeding for allegedly lying to Congress to justify the Iraq war, or Barack Obama charged with murder for killing US citizens abroad by drone strikes or US President Joe Biden charged with unlawfully inducing immigrants to enter country illegally, based on his border policies.
