Police in Ohio are investigating the motives of an armed man who they say tried to breach the FBI’s Cincinnati office, fled and died hours later in a rural stand-off with officers.

The FBI is warning agents to take extra precautions amid increased social media threats to its employees and facilities.

Officials have warned of the rise in threats against federal agents in the days following a search of former President Donald Trump’s Mar-a-Lago estate in Florida.

In Cincinnati, officials said a man tried to breach the visitors’ screening area at the FBI office on Thursday morning and fled when agents confronted him.

He was later spotted by a state trooper on an interstate and fired shots as the trooper chased him, said Ohio State Highway Patrol spokesman Lt Nathan Dennis.

The suspect eventually got out of his car on a rural road, exchanged gunfire with police and died at the scene, Lt Dennis said. No one else was hurt.

He said he could not comment on whether the suspect said anything to officers during the stand-off.

The man is believed to have been in Washington in the days leading up to the January 6, 2021, insurrection and may have been present at the Capitol on the day of the attack, according to an official.

The suspect was identified as Ricky Shiffer, 42. He was not charged with any crimes in connection with the Capitol attack, the official said.

Investigators are examining whether Shiffer may have had ties to far-right extremist groups, including the Proud Boys.

There have been growing threats in recent days against FBI agents and offices across the country after federal agents executed a search warrant at Mar-a-Lago. On Gab, a social media site popular with white supremacists and antisemites, users have warned they are preparing for an armed revolution.

FBI director Christopher Wray denounced the threats as he visited another FBI office in Nebraska on Wednesday.

“Violence against law enforcement is not the answer, no matter who you’re upset with,” Mr Wray said.

The warning did not specifically mention this week’s search of Mar-a-Lago but attributed the online threats to “recent media reporting on FBI investigative activity”.