Philippine President Ferdinand Marcos on Monday vowed to fight back against what he called reckless and troubling threats against him, speaking out after his estranged vice president said he would be assassinated if she herself were killed.

In a strongly-worded video message addressing the nation, Marcos did not name Vice President Sara Duterte, his presidential running mate, but said "such criminal plans should not be overlooked."

In a dramatic twist in fierce spat between Marcos and the powerful Duterte family, the daughter of firebrand former President Rodrigo Duterte on Saturday said she had instructed an assassin to kill Marcos, his wife and the lower house speaker, in the event that she were killed.

She was responding to a question during an online press conference about whether she feared for her safety. She did not cite any specific threat against her.

"The statements we heard in the previous days were troubling," Marcos said on Monday. "There is the reckless use of profanities and threats to kill some of us."

"I will fight them," he said, adding he would now allow such criminal attempts to pass.

"If planning the assassination of the president is that easy, how much more for ordinary citizens?"

Sara Duterte told reporters she had yet to hear the president's statement but would respond later.

Dutertes under scrutiny

Her stunning remarks were the latest salvo in an bitter row that has intensified since the collapse of a formidable alliance between their two powerful families that saw Marcos, the son and namesake of the Philippines' late authoritarian leader, win the 2022 election by a huge margin.

She quit her cabinet post in June and has battled against legislative scrutiny of her spending while in office, at times responding with open hostility to lawmakers and failing to show up for some proceedings.

Her threat to have Marcos killed stemmed from an order by lawmakers to transfer her chief-of-staff to a jail for allegedly impeding its probe over the vice president's alleged misuse of public funds.

According to a senior justice department official, the vice president does not have immunity from prosecution.

Marcos said it was vital for the interests of good governance that elected officials do not impede the work of legislators, adding "we will not have reached this drama if legitimate questions by Congress were answered".

Sara Duterte's attack on Marcos also comes just weeks after the mercurial Rodrigo Duterte was the subject of marathon enquiries in the house and Senate into thousands of killings during the notorious "war on drugs" that defined his 2016-2022 presidency.

During those hearings, the Marcos administration for the first time signaled it would cooperate with any international effort to arrest the former president, who is being investigated by the International Criminal Court (ICC) for possible crimes against humanity.

Rodrigo Duterte told the hearings he was solely responsible for the bloody crackdown and has urged the ICC to "hurry up" on its probe.