"All the pilgrims who came by land are now in Saudi Arabia. We extend our thanks to the Saudi king."
Al-Bayati had said that about 1,205 legitimate pilgrims had been prevented from crossing the remote Arar border post.
He said: "The problem is that some pilgrims were not able to fly for the lack of space on our planes.
"At least four Iraqi pilgrims have died of cold and hunger at Arar.
"Iraq is allowed to send 32,000 pilgrims. Iraq has not exceeded that quota."
In Riyadh, a Saudi official did not explain why the pilgrims had been denied entry, but said the kingdom always admits Iraqi pilgrims with valid visas.
The official, who spoke on condition of anonymity because he was not authorised to speak to the media, said about 12,836 Iraqi pilgrims had crossed the border to perform hajj this year.
Under a quota formulated by the Organisation of the Islamic Conference, Saudi Arabia issues 1,000 visas for every million people in a particular country.
Last year Iraq's Shia-led government accused Saudi Arabia of blocking some Iraqi pilgrims.
But Prince Nayef bin Abdul Aziz, the interior minister, rebuked the Iraqis for sending more than their quota of pilgrims.
Neither Iraqi nor Saudi officials have said whether the stranded pilgrims were Shia or Sunni Muslims.
Privately, Saudi officials have accused the Baghdad government, which is Shia-controlled, of giving more visas to Shia pilgrims than to Sunnis. The Iraqi government denies this.