Families of those held in Iran have accused Tehran of "hostage taking" and demanded governments take concerted action.
"It is clear to us that Iran bears responsibility for this attack. There is no other plausible explanation," Britain, France and Germany said.
In an interview with "NBC Nightly News" anchor Lester Holt, the Conservative prime minister praised President Donald Trump's negotiating skills.
US President Donald Trump on Friday approved sending American troops to bolster Saudi Arabia’s air and missile defences after the September 14 attacks on Saudi oil sites.
Riyadh and the U.S. have blamed Iran for the drone attack on 14 September.
Drone strikes on key Saudi oil installations last Saturday have reduced the flow of the world's oil supplies by about five percent.
Iran's Revolutionary Guards have seized an oil tanker headed for the United Arab Emirates for allegedly smuggling 250,000 litres of diesel fuel, the Iranian Students' News Agency (ISNA) reported on Monday.
Russia, Iran and Turkey will meet in Ankara on Monday to discuss how to improve the situation in north-west Syria
Two British-Australian nationals and one Australian national have been detained in Iran as tensions mount with the West.
Euronews' Anelise Borges spoke to a group of young Iranians about their prospects for the future, the Iran nuclear deal, and their country's friends and foes.