* UK says it will re-open Tehran embassy
* Embassy was shut after mob ransacked it in 2011
* Election of new Iranian president has thawed ties
* West, UK looking for Iran to help in Iraq (Recasts, updates after Hague comments to parliament)
By Andrew Osborn and William James
LONDON, June 17 Britain said on Tuesday it would re-open its embassy in Iran "within months," after a hiatus of more than two and a half years, a diplomatic breakthrough that underscores the West's desire to secure Tehran's help in Iraq and elsewhere.
The move came after the United States, a close British ally, said it may launch air strikes and act jointly with arch-enemy Iran to shore up the Iraqi government, after a rampage by Sunni Islamist insurgents that has scrambled alliances in the Middle East.
The announcement, by British Foreign Secretary William Hague, is likely to raise hopes of a breakthrough in talks with world powers about Iran's disputed nuclear programme. It coincided with negotiations aimed at securing such a agreement.
Britain severed direct diplomatic relations with Iran after activists stormed its embassy in Tehran in late 2011. The 2013 election in Iran of a relative moderate, President Hassan Rouhani, who replaced hardliner Mahmoud Ahmadinejad, paved the way for a thaw in ties.
Hague said that Britain would move quickly to re-establish a small initial presence at the Tehran embassy but said it wouldn't be able to offer visa services to Iranians at first.
"Iran is an important country in a volatile region, and maintaining Embassies around the world, even under difficult conditions, is a central pillar of the UK's global diplomatic approach," Hague said in a written statement to parliament. "I have ... now decided the circumstances are right to reopen our embassy in Tehran."
Hague said he had discussed the matter with Iranian Foreign Minister Mohammad Javad Zarif on Saturday and stressed the need for embassy staff to be able to work without hindrance in Tehran.
The decision did not mean Britain was "softening" any of its policies towards Iran, he said.
"We look to Iran to cease support for sectarian groups elsewhere in the Middle East, to reach a successful conclusion to nuclear negotiations. But I do believe it is important to discuss such issues with Iran and we need the ability to do so."
Calling for Iran to take a "more realistic approach" to nuclear talks, Hague urged Iran to improve its ties with its neighbours including the Gulf states to try to defuse tensions in the region.
"Iran does have the capability to play a more positive role across the region," Hague said. "It has played for many years a divisive and sectarian role through supporting divisive or often terrorist groups in other parts of the region."
It was now time for it to change tack, Hague said.
Britain's two diplomatic compounds in Tehran were overrun on an afternoon in November 2011 in what London said was a co-ordinated attack, after a rally against British sanctions escalated into violence and protesters scaled the walls.
Although the protesters withdrew after a rampage lasting several hours, Britain immediately withdrew all staff, closed the embassy, and ejected Iranian diplomats from London.
It was the worst crisis between Britain and Iran since full diplomatic relations were restored in 1999, a decade after Ayatollah Ruhollah Khomeini's fatwa that British author Salman Rushdie should be killed for writing "The Satanic Verses."
Indirect diplomatic ties were revived in November last year when Britain appointed a non-resident charge d'affaires.
Hague has ruled out any military involvement in Iraq by Britain, but he said a British "operational liaison and reconnaissance team" arrived in Baghdad at the weekend and that Britain would provide humanitarian assistance as needed.
He has said that as many as 400 British citizens may be fighting in Syria and that some may also be fighting in Iraq with ISIL, the Islamic State of Iraq and the Levant. (Editing by Larry King)