The call late last Thursday follows Saudi Arabia, home to Islam's holiest cities of Mecca and Medina, announcing electronic registration for Qatar residents to allow them to perform the Umrah or minor pilgrimage during the holy month of Ramadan.
Qataris and foreign residents of the Persian Gulf state would then be allowed to land at Jeddah or Medina airports, said a statement carried by the official Saudi Press Agency on Tuesday.
But Qatar's National Human Rights Committee said the new measure was "nominal" and insufficient, as air travel remained blocked and the only border post has been shut for almost two years. Its Ministry of Islamic Affairs, meanwhile, called on Saudi authorities "to lift all obstacles and restrictions imposed on Qatari citizens and residents wishing to perform their religious rituals."
The travel restrictions mean Qatari religious tour operators are unable to travel to Saudi Arabia to make the necessary arrangements for pilgrims, like other countries, the ministry said.
The ministry also called for the removal of "discriminatory" measures against Qataris and residents of the Persian Gulf state.
Some 12,000 Qataris performed Hajj in September 2016, but months later Saudi Arabia and its allies cut ties with Qatar and imposed a blockade over its alleged support for radical groups.
A few dozen Qatari pilgrims have travelled independently to Saudi Arabia over the past two years, when the Saudis briefly opened the only border post between the two countries for pilgrims.