The king has permitted "the entry of Qatari pilgrims to the Kingdom of Saudi Arabia through Salwa border crossing to perform hajj, and to allow all Qatari nationals who wish to enter for hajj without electronic permits", a statement on SPA said.
Qatar welcomed Saudi Arabia's decision to reopen the Salwa border to Haj pilgrims, but called it "politically motivated".
SPA said the king's decision was "based on the mediation efforts of Sheikh Abdullah bin Ali bin Abdullah bin Jassim Al Thani, a member of Qatar's ruling family".
Saudi Arabia, and UAE reportedly tried last month to drag Baghdad into the spat but Abadi pushed off their requests.
A statement released by the Presidency, Puntland state of Somalia formally declared it has sided with the Kingdom of Saudi Arabia and the United Arab Emirates (UAE) against Qatar.
Saudi Arabia had said earlier it would only allow Qatari pilgrims to arrive on flights from Doha, leading Qatar to accuse Saudi Arabia of politicizing the process.
Some 127,198 pilgrims were scheduled to perform hajj from Bangladesh this year under government and private managements.
"All Qatari pilgrims be transported from King Fahad International Airport in Dammam and Al-Ahsa International Airport as his (King Salman) guests".
The committee expressed its "satisfaction" with the decisions, but reiterated its demands that the hajj not be politicized and said the Saudi measures remain "unclear", particularly regarding the facilitation of hajj for foreigners residing in Qatar. Saudi Arabia prides itself on hosting millions of pilgrims annually at Islam's holiest sites in Mecca and Medina.
The quartet accuses the small Gulf nation of supporting extremists. Mecca is in Saudi Arabia, but Qataris were not allowed to fly there directly from Doha under the sanctions prior to the king's order.
Qatar has denied the accusation.
Spokesman of the state Hajj team, Mr Jubril Gomna, told the News Agency of Nigeria (NAN) in a telephone interview that the pilgrims left the Nnamdi Azikiwe International Airport Abuja, on Tuesday, at about 10.40am.
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