Tehran has rejected any involvement in Sunday's incident at the US-used airbase, where police found petrol but no explosives and five suspects have been released on bail.
British Prime Minister Andy Burnham said on Wednesday there were "strong indications" that Iran was involved in suspicious activity near a UK airbase used by the US military, which sparked a major security alert.
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"There are strong indications that Iran played a part in what happened over the weekend at RAF Fairford," Burnham told the BBC, referring to Sunday's bomb scare near the base in southwest England, which the US has been using in its war against Iran.
"Of course it remains an ongoing, complex, and serious police investigation," he added.
Speaking to Sky News, Burnham said: "We have been waiting to confirm what we could say, but we can now confirm our belief that Iran played a part."
His remarks are the first official indication from UK authorities that Iran may have been behind the incident. Officials have not explained the nature of the threat.
Iran's embassy in London had earlier said it "categorically rejects and strongly condemns" speculation that it was involved.
The alert began in the early hours of Sunday, when three white vans appeared to be heading towards RAF Fairford. A local resident who called the police said she saw a group of masked men near the vans, which were blocking a road in a village next to the base.
Police arrested five British men on Sunday on suspicion of explosives and terrorism offences, but later released them on bail.
On Tuesday, after three days of investigations that included deploying a bomb disposal team, police said no explosives had been found in the vehicles, although they had recovered a "quantity of petrol".
US President Donald Trump and Secretary of State Marco Rubio had previously suggested that intelligence services were aware of the suspects and that a foreign state could be involved, but UK officials had until now not commented.
Speculation had mounted that Iran or another hostile state could be responsible, after Tehran warned London against allowing its military bases to be used by Washington.