Britain is set to reopen its embassy in Iran, Foreign Secretary William Hague announced on Tuesday.

The move came as the West steps up its engagement with Iran amid rapid rebel advances in neighbouring Iraq.

Rebel fighters from the Islamic State of Iraq and the Levant (ISIL) have threatened to advance on the Iraqi capital Baghdad after a week-long offensive which has seen them make key gains, including taking the second city of Mosul.

"I have therefore now decided the circumstances are right to reopen our embassy in Tehran. There are a range of practical issues that we will need to resolve first," Hague said in a written statement to parliament.

"However, it is our intention to reopen the Embassy in Tehran with a small initial presence as soon as these practical arrangements have been made."

His statement did not directly mention the situation in Iraq, but noted that "Iran is an important country in a volatile region".

The Iraqi Prime Minister Nouri al-Maliki, a Shia, is considered close to Tehran, and the West is exploring to involve Iran in order to form joint fight against the Sunni rebels.

Pentagon spokesman, RADM John Kirby, said on Monday that the US was open to political discussions with Iran, but not military cooperation, according to NBC news.

Britain closed its embassy in Tehran in 2011 after it was stormed by a mob, and suspended full diplomatic relations with the Islamic republic.