MECCA, SAUDI ARABIA—Saudi Arabia sought to assure the public that the kingdom was safe and free of health scares as an estimated 2 million Muslims streamed into a sprawling tent city near Mecca on Thursday for the start of the annual Islamic hajj pilgrimage. Earlier this year, Saudi authorities banned people from Sierra Leone, Liberia and Guinea — the countries hardest hit in the Ebola epidemic — from getting visas as a precaution against the virus. The decision has affected a total of 7,400 pilgrims from the three countries. Ebola is believed to have sickened more than 7,100 people in...