Mr Khamenei was killed in his office after it was hit by missiles on Saturday.
The timing of Asake’s return comes amid military tensions in the Middle East, where the United States and Israel launched an attack on Iran.
A 40-day mourning period has been declared for Mr Khamenei.
She accused Mr Trump of reneging on his campaign promise to end foreign wars.
Israeli Prime Minister Benjamin Netanyahu had said there were many signs Mr Khamenei had been killed in the strikes targeted against his residence.
The Israeli prime minister said Israel, in collaboration with the U.S., coordinated the bombing of Iran on Saturday.
The police spokesperson said one locally made pistol and two live cartridges were recovered from one of the suspects.
Mr Youssouf appealed to the warring countries to adopt dialogue and abide by international law and the United Nations Charter.
Earlier on Saturday, the U.S. and Israel launched deadly airstrikes on Iran.Â
