"The legal process has been launched, and if their guilt is proved, they will face punishment," Gholam Reza Ansari said in an interview with Russia's satellite channel Vesti 24.
Iran detained 15 British seamen in the Gulf last Friday for violating its maritime border with Iraq. Britain has insisted the servicemen were in Iraqi waters under a UN mandate, and were returning in dinghies to the HMS Cornwall after patrolling oil platforms.
Ansari said the problem could have been resolved if the U.K. acknowledged the border violation and offered an apology.
"If the government of Britain had offered an apology to Iran for the mistake, the issue could have been resolved immediately," the diplomat said.
London froze official bilateral contacts, suspended the issuance of visas to Iranian officials and referred the situation to the UN Security Council Wednesday. The UN expressed "grave concern" over the sailors' capture.