It took more than two hours for the cortege to make its way through the crowds to the south Tehran mausoleum where Rafsanjani was laid to rest.
Pallbearers accidentally knocked the former president's trademark white turban off the coffin as they carried it into the burial chamber at the mausoleum of Ayatollah Ruhollah Khomeini, leader of Iran's 1979 Islamic revolution.
Rafsanjani, who served as president from 1989 to 1997, was a father figure for Iran's moderate and reformist camps.
Rouhani, who spearheaded the thaw with the West that culminated in a 2015 nuclear deal, faces a tough re-election battle in May amid disappointment over the smaller than anticipated economic dividends of the lifting of international sanctions.
Supreme leader Ayatollah Ali Khamenei led the eulogies to Rafsanjani at Tehran University despite their "differences".
Rafsanjani fell out of the regime's highest inner circle following the 2009 re-election of hardliner Mahmoud Ahmadinejad, when he spoke out against the use of lethal force on protesters who claimed the vote was rigged.
One of Iran's most controversial figures in the West, the head of the elite Revolutionary Guards' foreign operations division, Major General Qassem Suleimani, also attended.
Tehran prayer leader Ayatollah Mohammad Emami Kashani passed out and had to be treated at the scene by Health Minister Hassan Ghazizadeh Hashemi, an ophthalmologist by training, Iranian media reported.
Reformist former president Mohammad Khatami, an ally of Rafsanjani but long out of favour with the regime, was not part of the official delegation.
State television coverage of the funeral procession captured a few seconds of chants of "Hail Hashemi (Rafsanjani), hail Khatami," before the broadcaster drowned it out with solemn music.
Video clips published on social media showed pockets of mourners in the streets chanting slogans in support of both Khatami and fellow reformist Mir Hossein Mousavi.
Mousavi and Mehdi Karoubi, two of the losing candidates in the 2009 election, have been under house arrest since 2011 for leading the so-called Green Movement protests that the regime calls "sedition".
Khatami is under a strict media ban and is often prevented from attending public events.
"Ayatollah Rafsanjani's concern was unity... And we should show off our unity to the world," he said on Monday.
Black banners were raised in Tehran and some posters showed the supreme leader and Rafsanjani together smiling. Another poster said "good bye, old combatant".
Since Rafsanjani's death, messages of condolence have poured in both from at home and abroad.
Even the White House sent a message, unprecedented since the 1979 revolution that led to cutting of ties between Tehran and Washington.
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