An official statement, carried by the state-run Iraqi News Agency, vowed "suitable response" if the United States interfered with the flights.
The White House warned Iraq against violating the no-fly zone, but said it would not attack the helicopters.
Western allies introduced the no-fly zone after Iraq's defeat in the 1991 Gulf War. It is meant to protect inhabitants of southern Iraq from reprisals by President Saddam's army after an unsuccessful anti-government revolt in the area.
The zone was extended in September to punish President Saddam for sending his army into northern Iraq to support one Kurdish faction against another. It now covers an area stretching from the southern suburbs of Baghdad down to Iraq's borders with Kuwait and Saudi Arabia.
The Iraqi News Agency said helicopters would begin ferrying "sick and exhausted" pilgrims yesterday, but did not say how many aircraft would be involved or give the number of pilgrims.
But, by nightfall, there was no word from Iraqi officials or the state- run media if any flights had taken place and reporters in Baghdad were told by officials they would be flown to the Saudi border today.
The decision to use helicopters to ferry home the pilgrims was made after a joint meeting yesterday of the Revolutionary Command Council and the leadership of the ruling Baath Party - Iraq's highest bodies. The meeting was chaired by President Saddam.
On 9 April, President Saddam sent an Iraqi Airways jet carrying 104 pilgrims to Saudi Arabia in defiance of United Nations sanctions imposed in 1990 for Iraq's invasion of Kuwait. The sanctions ban flights in and out of Iraq.
The United States failed last week to persuade the Security Council to condemn the Iraqi flight, settling instead for a mild rebuke.
Yesterday's announcement is the latest of several attempts by the Iraqi leadership to test the resolve of the international community, particularly the United States, to maintain Iraq's isolation.Reuse content