Millions of people attend the annual Hajj, due this year in November.
The Muslim religious authorities in Egypt have suggested delaying the annual pilgrimage to Mecca because of the spread of swine flu.
Egypt's Grand Mufti, Sheikh Ali Jumua, has called for a religious edict to decide how long the pilgrimage rites of the Hajj could be postponed.
At least two million people took part in the last Hajj, which falls this year in November.
More than 7,500 cases of swine flu have been reported worldwide.
In an interview with BBC Arabic radio, Dr Ibrahim Negm, an advisor to the Grand Mufti, said Sheikh Ali Jumua supported a view already outlined by Mohammed Tantawi, the Grand Imam of the al-Azhar Mosque.
Mr Tantawi says that the pilgrimage rites could be postponed if the World Health Organisation declares a global pandemic, and raises its pandemic alert from five to the maximum six.
At that point, he says, Islamic researchers would meet to discuss a possible delay.
A Malaysian student is in hospital in Kuala Lumpur suffering from swine flu
Mr Negm insisted however, that both the Grand Mufti and the Imam believed this was a technical issue, which should be dealt with by the ministries of health, environment and agriculture.
The Mufti of the United Arab Emirates, Sheikh Abdel Aziz Haddad, has urged Muslims to delay any pilgrimage to Mecca for the next two or three weeks.
He also advised the faithful to pray in the open air to avoid contracting, or spreading, the swine flu.
As well as the annual Hajj pilgrimage, which all Muslims are required to make at least once if they have the means, the faithful can also make a lesser pilgrimage to Mecca, known as umra, at any time of the year.
No cases of swine flu have been reported in any Gulf or Arab countries. But pilgrims travel to Mecca from around the world, including countries where the swine flu virus has been confirmed.
The WHO says the number of confirmed swine flu cases has risen by more than 1,000 in the last 24 hours. More than 7,500 people have gone down with the flu, in 34 countries, and 65 people have died, mainly in Mexico, where the outbreak began.
Malaysia has confirmed its first case of swine flu - a student who arrived on a flight from the United States on Wednesday. The authorities are trying to trace the 199 passengers and crew from the flight, though they believe some of them may have travelled on to Indonesia.