State TV 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 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.
On Sunday, tens of thousands more mourners, including soldiers, seminary students and ordinary men and women filed into the Mosalla to pay their respects to Khamenei and his family, waving flags emblazoned with promises of revenge against the US and Israel.
Others prayed in unison at the complex named after Iran's first supreme leader Khomeini, whom Khamenei succeeded in 1989.
The farewell ceremony was extended by about an hour to 10pm due to the high number of people taking part, state media reported.
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.
One disappointed mourner said she had hoped to see the new supreme leader during the funeral events.
"Until the last moment, before the prayer began, I kept telling those around me that I hoped (Mojtaba Khamenei) himself would come. That was our only wish," a young woman wearing makeup and sunglasses told the Tasnim news agency in an interview.
A ceasefire has suspended the four-month-old war under an agreement with the US that Iran's authorities say will ultimately bring huge economic benefits, in line with what they describe as a victory over a superpower.
During the war, more than 3000 people were killed, including many of Iran's most senior politicians and military commanders.
Military bases and major infrastructure projects were destroyed causing billions of dollars in damage.
But Iran struck US bases in the region, inflicted pain on the Gulf Arab countries that host them and asserted its control of the Strait of Hormuz, causing a spike in global energy prices.
The interim deal reached last month includes the unfreezing of billions of dollars in Iranian assets held abroad and waivers from financial sanctions that had brought Iran's economy to its knees.
US President Donald Trump told the Axios news website that peace talks had been paused for a week for the events surrounding the funeral.
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.
