The ceremony saw 104 bodies returned home from Saudi Arabia. Iran says at least 464 of its nationals were killed.
The Saudi authorities put the total death toll at 769, but foreign media reports and officials put the figure at well over 1,000.
Tehran had blamed the incident on Saudi “mismanagement”.
But Saudi Arabia’s Foreign Minister, Adel Al-Jubeir, had accused Iran of “playing politics” with the disaster, calling on Tehran to await the outcome of an investigation.
Speaking at the repatriation ceremony, Iranian President, Hassan Rouhani, said that the tragedy was a “big test” for everyone. “In this incident, our language has been that of fraternity and respect”, he said.
“When required, we have used the language of diplomacy. If needed, the Islamic Republic of Iran will also use language of power.”
The crush happened as two large groups of pilgrims converged as they were taking part in one of the Hajj’s major rites.
The Saudi authorities have not released a breakdown of victims by nationality.