"Let's make the accidents at the stoning part of history, may it never return," state-run Saudi television reported in a programme about improvements to the bridge facilitates.
Saudi authorities have made renovations to ease the flow of pilgrims, adding a fourth platform from which to throw stones.
Al Jazeera's Sami Zeidan, reporting from Mina, said: "This year the pilgrimage does appear to be better organised, crowd flow is a lot smoother as people head to do the symbolic stoning of the devil.
"The atmosphere is beautiful, a sense of achievement and relief is in the air, and there is a spirit of celebration here."Spiritual climax
Saudi authorities have appealed to pilgrims to perform the ritual at any part of the day, rather than only in the afternoon, in an attempt to ease the crush.
"This crowdedness is really scary," Umm Mohammad, a Syrian pilgrim, said as she watched the twisted trail crowded with pilgrims from the top of a flyover in Mina.
Although no major accidents or incidents have been reported at the Hajj this season, the Saudi authorities were not able to stop some political activities, which pilgrims had been warned to avoid.
|A record 1.72 million pilgrims came from abroad this year [AFP]
Iranian television showed Iranian pilgrims at Arafat chanting "death to America" and "death to Israel" on Sunday.
Ayatollah Mohammad Mohammadi Reyshahri, head of Iran's haj mission, said Islam was now resurgent, despite some Muslims' despair "in the face of Western civilisation's onslaught".
Monday is the start of the Eid al-Adha, or feast of the sacrifice, commemorating the willingness of biblical patriarch Abraham to sacrifice his son for God.
Some pilgrims who had completed the first round of three stoning rituals late on Sunday, performed Eid prayers at the Grand Mosque, after men shaved their heads and bought sacrifical animals, marking the end of the Hajj climax.
On Sunday, pilgrims spent the day in prayer at Mount Arafat 15km east of Mecca, where the Hajj reached its spiritual climax.
As part of its intensified crowd control measures, the Saudi government has been tougher this year in preventing Saudis and foreign residents from taking part without official Hajj permits.
The Saudi media said a record 1.72 million pilgrims had come from abroad this year, and more than half a million had come from inside the country, home to Islam's holiest sites.