Mr Marcos Jr is the son of late Philippine dictator Ferdinand Marcos, who ruled the country under martial law before being overthrown in a popular uprising in 1986.
After making a pact to win the election, the pair have had a serious falling out over disagreements in policy approaches, including how Manila should handle Chinese territorial aggression in the international waters of the South China Sea.
The Philippine presidential security command said it considered Ms Duterte’s threat a matter of national security, and immediately boosted its security for Mr Marcos Jr.
The security force said it was “co-ordinating with law enforcement agencies to detect, deter and defend against any and all threats to the president and the first family”.
Ms Duterte has also opposed Mr Marcos Jr’s wife, Liza Araneta-Marcos and house speaker Martin Romualdez, alleging corruption, incompetence and political persecution of her family and their allies.
Her assassination threat comes shortly after Zuleika Lopez, her chief of staff, was detained by Mr Marcos Jr’s allies in the house.
Ms Lopez is accused of impeding a congressional inquiry into whether she misused the budget in her prior posts as vice-president and education secretary.
The dramatic political spat has prompted Romeo Brawner, the Philippine military chief, to assure that the country’s armed forces remained non-partisan and retained “utmost respect for our democratic institutions and civilian authority”.
“We call for calm and resolve,” Mr Brawner said. “We reiterate our need to stand together against those who will try to break our bonds as Filipinos.”