Despite their worries earlier this year, world health authorities say there is little reason to fear that the annual Muslim pilgrimage to Mecca in Saudi Arabia, which began Thursday, will spread the MERS virus widely around the world. But they are emphasizing that vigilance is still important.

The World Health Organization’s emergency committee on Middle East Respiratory Syndrome concluded on Wednesday that the outbreak, concentrated on the Arabian Peninsula, did not constitute an international health emergency.

Separately, the risk of Ebola at the pilgrimage appeared low. Saudi Arabia has denied visas to all would-be pilgrims from Guinea, Liberia and Sierra Leone, the three countries suffering major outbreaks. An unrelated Ebola outbreak in the Democratic Republic of Congo is in an isolated rural area.

This past spring, Saudi Arabia had hundreds of MERS cases. But there were only 15 known cases from mid-August to late September, the W.H.O. said. None were in the three cities visited by virtually all pilgrims — Jidda, Mecca and Medina.