Gibraltar said it had reasonable grounds to believe Grace 1 was carrying crude oil to the Baniyas refinery in the war torn Middle East nation.
The tanker was making its way through narrow waterway when the Iranian ships approached.
It added: "It would be highly unlikely for Iran to persist in any attempt to detain a vessel in worldwide waters or to engage a vessel with weapons".
"The situation is very concerning", said Russia's Deputy Foreign Minister Sergei Ryabkov, quoted by news agency RIA Novosti.
The Revolutionary Guards said there had been no confrontation with foreign ships, including from the United Kingdom, in the past 24 hours, the semi-official Fars news reported. "In the last 24 hours, we had no incident involving foreign vessels in the Strait of Hormuz, also not with a British one", a statement said.
British "claims that have been made are for creating tension and these claims have no value", Zarif said.
Why are UK-Iran tensions escalating?
"US and UK's measure to seize Iran's oil tanker was in violation of worldwide laws and this act will bring disgrace upon them".
Iran earlier described the seizure of Grace 1 as an act of "piracy" and accused Britain of bowing to United States pressure to hinder its attempts to export oil under the terms of the 2015 nuclear deal.
Earlier, Iranian President Hassan Rouhani said Britain would face "consequences" over the seizure of the Iranian tanker.
"You are the ones initiating insecurity, and will come to realize its consequences in the future", Iran's state-run Press TV reported.
Supreme Leader of Iran, Ayatollah Ali Khamenei making a speech in Iran, on 5 June, 2019. "While we are not commenting on these events, we thank the Royal Navy for their support".
This is enough to provide reassurance, but probably not to deal with a crisis, BBC defence correspondent Jonathan Beale said.
There are six vessels operating in the Persian Gulf registered to Britain, or a British Overseas Territory, and five operating under the British flag.
The Iranian Revolutionary Guard, which patrols the waters, denied that any incident had taken place.
The vessel is registered at the port of Douglas, in the Isle of Man.
"Capture of the Iranian oil tanker based on fabricated excuses. will not be unanswered and when necessary Tehran will give appropriate answer", Bagheri said, The Telegraph reports.