The group was preparing to board a flight on Saturday at Portland International Airport, when Abd Allah Abbasi left to get a cup of coffee, leaving a carry-on bag behind.
Before he returned, the rest of the group had boarded and someone had reported his unattended baggage.
Before he returned to collect his bag, Abbasi was detained, despite his colleagues' protests, reported The Oregonian newspaper. Apparently there were language difficulties and the crew could not understand the parliamentarians.
The pilot ordered the Moroccans off the flight and the Transportation Security Administration (TSA) became involved.
Officials became alarmed when they saw documents in Arabic with the group's luggage with 911 written on them. Later it was discovered that a host in Dallas, a previous stop, had given them instructions to dial 911 on the telephone, the number for US emergency services, if they got into trouble.
It was mistaken for a reference to the 11 September 2001 attacks in Washington and New York, often shortened to 9/11.
When an FBI interpreter finally arrived, he questioned the group. The visitors were not deemed a security threat.
They missed a connecting flight and spent all day at the airport before boarding another flight.
Andrew Coose, the TSA's deputy security director in Portland, said the incident was "absolutely unfortunate," but that the agency was not equipped to handle such an incident quickly.
The Moroccans were frustrated because they carried diplomatic passports and Delta airline officials were aware of their status.
"I'm very embarrassed, I'm really frustrated by their treatment here today," said Multnomah County Commissioner Serena Cruz. "They're national elected officials."
Security has been tight at airports across the United States, for fears of more September 11-style attacks.
US carrier Continental Airlines cancelled a flight from Washington to Houston, Texas on Sunday, one day after it and two other airlines grounded 10 intercontinental flights due to security threats.