State TV on Sunday showed Mostafa, Meysam and Masoud Khamenei praying behind the coffins laid out in the vast courtyard of Tehran's Imam Khomeini Grand Mosalla, a sprawling religious complex.
Their father, alongside several other members of the family, was killed in an air strike when the United States and Israel launched a war on Iran on February 28.
The conflict, which raged for several weeks before the sides reached a shaky ceasefire, has caused death and destruction across the region and left Iran's theocratic government, backed by the Islamic Revolutionary Guards Corps, in power.
In a show of public devotion to the theocratic state and revolutionary zeal, the Islamic Republic is staging a week of mass funeral processions for Khamenei, including taking his remains to Shi'ite religious sites in neighbouring Iraq.
After a day lying in state indoors for senior Iranian leaders and foreign officials to visit, Khamenei's coffin was displayed outdoors on Saturday under glass, along with those of his daughter, son-in-law, daughter-in-law and 14-month-old granddaughter.
There has still been no public sighting or image released of Mojtaba, said to have been injured in the attack that killed his father and the other family members on February 28, when Israel and the US bombed Iranian targets at the start of the war.
Mojtaba Khamenei's face was disfigured and he suffered a significant injury to one or both legs, people close to his inner circle told Reuters.
A ceasefire has suspended the four-month-old war under an agreement with Washington that Iran's authorities say will ultimately bring huge economic benefits, in line with what they describe as a victory over a superpower.
US President Donald Trump told the Axios news website peace talks had been paused for a week for the events surrounding the funeral.
On Sunday, Iranian President Masoud Pezeshkian and Parliament Speaker Mohammad Baqer Qalibaf prayed behind the coffins.
Masoud Khamenei was seen crying and wiping his tears with a keffiyeh - the chequered scarf that is a symbol in Iran of militant revolutionary ideals and solidarity with Palestinians - as an imam recited funeral prayers.
Crowds of Iranians, many weeping and some beating their chests, have thronged the Mosalla, including overnight.
The Iranian metro railway network said it had clocked seven million trips from late on Saturday to Sunday morning as people flocked to the centre.
After what authorities are billing as a massive procession in central Tehran on Monday, the remains will be taken to the seminary city of Qom, the centre of Iran's Shi'ite hierarchy, for ceremonies on Tuesday.
From there, the body will be flown to Iraq for ceremonies in the Shi'ite holy shrine cities of Najaf and Kerbala on Wednesday.
It will return to Iran on Thursday for another procession in Mashhad, to be buried near the tomb of another of the medieval Shi'ite imams.
Authorities plan to mobilise millions of people for big processions in the coming days, offering transport, food and lodging.
