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By Inal Ersan

MENA, Saudi Arabia, Dec 10 (Reuters) - More than two million Muslims performing the haj pilgrimage entered the final stage of the rituals on Wednesday, visiting the Grand Mosque in Mecca and stoning walls representing the devil one more time.

For a third day pilgrims threw stones at the Jamarat Bridge in the valley of Mena outside the Islamic holy city of Mecca, which has been the scene of numerous stampedes in past years, including one which killed 362 in 2006.

The haj also has been marred in previous years by deadly fires, hotel building collapses and police clashes with protesters. More stringent security and crowd control this year appeared to have paid dividends, though there were still lapses.

"God makes things easy. The expansions have reduced crowding a little," said Mohammad Mousa, an Egyptian teacher and father of two pushing a twin pram by a pilgrim bus.

"Praise be to God -- things are smooth, we've not heard of any incident. The flow of pilgrims is moving very well," said Saudi preacher Ali Hussein Sawadi Mashour.

Saudi Arabia, Islam's birthplace and home to its holiest sites, has erected a massive four-level building with several platforms for throwing the stones at three walls in an ancient rite marking chapters of the story of the prophet Ibrahim -- the biblical Abraham -- in Mecca and the rejection of temptation.

The unfinished bridge is now a huge air-conditioned building the size of an airport terminal. Expansions also have been made to the Grand Mosque in Mecca.

Authorities have appealed to pilgrims to throw their stones at any time of day rather than only in the afternoon, as Saudi clerics often insisted in the past.

The sidewalks were filled with pilgrims who were praying, sleeping, eating, brushing their teeth or chattering ahead of the stoning ritual in the afternoon.

"I'm not scared of the crowds. I went to finish early before sunset, to leave room for other pilgrims," said Ramadan al-Habisi from Egypt.

Some people managed to enter the area to perform haj without official permits and set up makeshift camps on the road which have been a cause of overcrowding before.

"Sleeping on pavements is banned. Brothers, fathers, pilgrims -- please take a bus or walk to the tents," policemen repeatedly urged pilgrims through a loudspeaker.

One woman protested, pressing a reporter to intervene.

"Tell them to let us sleep here. It will be only a night or two, no harm done," said Sabiha, sitting on a pavement next to her son, an Egyptian who lives in Saudi Arabia and was performing haj without a permit.

At least 2.4 million worshippers from all over the world came to Mecca this year, including a record 1.72 million pilgrims from abroad, Saudi media reported.

Saudi Arabia grants haj visas to countries according to strict quotas but has increased the numbers after the expansions. Every able-bodied adult Muslim who can afford the trip must perform the haj at least once in a lifetime, which means numbers are likely to grow further in coming years.

Haj, one of the largest manifestations of religious devotion in the world, retraces the path of Prophet Mohammad 14 centuries ago after he defeated pagan forces in Mecca. Islam is now embraced by more than one billion people worldwide.

(Editing by Samia Nakhoul)

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