The statement followed an expletive-laced press conference in which Duterte alleged she was the subject of an assassination plot and said she ordered a member of her security team to kill the president should it succeed.
The Duterte and Marcos families have seen their alliance unravel in spectacular fashion in recent months, trading accusations of drug addiction and increasingly extreme rhetoric ahead of next year's mid-term elections and presidential polls in 2028.
"I already talked to a person in my security. I told him if I get killed, kill BBM (Ferdinand Marcos), (first lady) Liza Araneta and (the president's cousin) Martin Romualdez. No joke," Duterte said at a press conference that began after midnight.
"I said, if I die, don't stop until you have killed them."
Hours later, the palace communications office said it had referred "this active threat to the Presidential Security Command for immediate proper action".
"Any threat to the life of the President must always be taken seriously, more so that this threat has been publicly revealed in clear and certain terms," it said in a statement.
Duterte is facing the threat of impeachment in the House of Representatives, led by Marcos's cousin Romualdez, who is widely expected to run for president in 2028.
She has also had a messy falling out with the president's wife Liza Araneta-Marcos, who has accused her of laughing at a January event where her father, former president Rodrigo Duterte, accused Marcos of being a "drug addict".
Duterte called her late-night press conference after House officials said they would transfer her chief of staff -- detained after being cited for contempt -- from the lower chamber's detention centre to a correctional facility.
Zuleika Lopez was detained on Wednesday after being accused of "undue interference" in House proceedings focused on Duterte's spending of public funds.
Duterte stepped down from the cabinet post of education secretary in June as relations between the two families reached a breaking point.
Months earlier, her father had accused Marcos of being a "drug addict", with the president the next day claiming his predecessor's health was failing due to long-term use of the powerful opioid fentanyl.
Neither provided evidence of their allegations.
In October, Duterte said she felt "used" after teaming with Marcos for the May 2022 election, which they won by a landslide.
Duterte remains the constitutional successor to the 67-year-old president.
