Assefi said the police are seriously investigating the incident, adding security has been beefed up around the embassy.
Unknown assailants fired shots at the British embassy in Tehran on Wednesday and the embassy temporarily closed the building for business.
Bullets hit windows in upper stories of the building which stand near the perimeter wall next to a busy Tehran street, embassy said. No one was injured.
British Foreign Ministry Spokesman, James Piwa, told the Mehr News Agency on Wednesday that London does not point fingers at anybody or group for attack on its Embassy in Tehran
"Currently Britain does not accuse any individual or group of attacking the British Embassy," Piwa said.
Piwa said that the bullets hit offices on the first and second floors of the building.
"Nobody was injured but the embassy has been temporarily closed for business," he stressed.
The spokesman added that the British Foreign Ministry is currently having talks with the Foreign Ministry of Iran.
He said that the Iranian government has to investigate the attack.
Elsewhere in his remarks Piwa said that Britain will announce its stance on the issue after the current talks with the Iranian Foreign Ministry are over.
The incident occurred at a time of rising tension between Iran and Britain over Britain's arrest of a former Iranian diplomat who has been detained by British police in connection with the 1994 bombing of a Jewish center in Argentina.
Iran's ambassador to London returned to Tehran for consultations following the row over the arrest of former diplomat Hadi Soleimanpour in connection with the Buenos Aires bombing which killed 85 people, Iranian and British officials said on Wednesday.
Iran has rejected any involvement in the Argentine case.
Staff at the British embassy in Tehran said up to six shots were fired but they said it was not clear who fired them.
On the diplomatic front, Britain said it understood the recall of Iran's London envoy, Morteza Sarmadi, did not mean a downgrading in relations.
Soleimanpour, who was Iran's ambassador to Argentina at the time of the 1994 bombing and who is in custody at Argentina's request, has protested his innocence.
Iran believes that Soleimnanpour’s detention is politically motivated and has promised "strong action," warning Britain that the issue would harm bilateral ties.
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MNA