Hoshyar Zebari's appeal came in a telephone conversation late on March 25 with his Iranian counterpart, Manuchehr Mottaki.
In a statement, the Iraqi Foreign Ministry said Zebari told Mottaki that the British personnel were detained in Iraqi waters and called on Iran to deal with the case in a "wise way."
Britain says the sailors and marines were conducting a routine search of shipping in a waterway that forms the southern border between Iraq and Iran.
Iran says they entered Iranian waters illegally and that it is considering bringing charges against them.
On March 25, British Prime Minister Tony Blair described the situation as "very serious" and said Iran's actions were "unjustified and wrong."
In comments on Iranian state television today, Iranian Deputy Foreign Minister Mehzi Mostafavi denied reports that the sailors might be swapped for Iranian detainees detained by U.S. forces in northern Iraq. He said the Britons were being interrogated.