Ecuadorean authorities declined to elaborate on Tuesday on the group's alleged links to "terrorist" activities "until further investigation".
But an internal police report said preliminary evidence "confirms the relationship between this organisation and the terrorist movement Hizb Allah".
The document said the gang sent "up to 70% of its profits to the Islamic group". It smuggled cocaine principally to Europe and Asia in shipments valued at US$1 million each, the report said.
Anti-narcotics police on Tuesday presented a lineup of the alleged Lebanese ringleader, Rady Zaiter, and five other male suspects from Lebanon, Syria, Nigeria, Algiers and Turkey, in addition to an Ecuadorean woman.
Some of the suspects tried to cover their faces with their handcuffed hands while local journalists took photographs.
The Ecuadorean investigation led to related arrests of 19 people in Brazil and the United States, the report said.
Brazilian authorities, however, said on Wednesday they had no evidence that 14 Lebanese arrested in their territory on Friday were connected to Hizb Allah.
"We have discovered nothing linking these people to Hizb Allah or to any other extremist group operating in the Middle East"
Brazilian police official
"We have discovered nothing linking these people to Hizb Allah or to any other extremist group operating in the Middle East," said Julio Bortolato, of Brazil's federal police.
According to the Ecuadorean police report, Zaiter "had organised a large narcoterrorist infrastructure", using his Arab food restaurant in northern Quito as a front.
He and Maher Hamajo, the Syrian who was arrested, allegedly used couriers who hid cocaine in suitcases and ingested it into their stomachs to smuggle the drugs into Europe, Asia and other South American countries.
The group "recruited" Ecuadorean airport officials to evade security checks, according to the report.
The report said police discovered four houses used by the suspects and seized two autos, two motorcycles, two pistols, two shotguns and US$174,115 in cash.
The US considers Hizb Allah a terrorist organisation, but the group is generally lauded in the Middle East for forcing the Israelis to withdraw from Lebanon in 2000.
Hizb Allah has yet to react to the allegations.