* Britain says it close to identifying Foley killer
* Iraq urges international effort against Islamic State
* Iran backs Baghdad's fight against the militants
By Babak Dehghanpisheh and Eric Beech
BAGHDAD/WASHINGTON, Aug 24 (Reuters) - Britain is close to identifying a suspected British national shown beheading American journalist James Foley in a video released by Islamic State militants last week, the British ambassador to the United States said on Sunday.
With Islamic State fighters now in control of vast areas of northern Iraq, the country's prime minister-designate, Haider al-Abadi, used a meeting with the visiting Iranian foreign minister to call for greater international efforts to destroy the Islamist group.
Foreign Minister Mohammad Javad Zarif of Iran, a Shi'ite Muslim power likely to wield influence over the formation of Abadi's new cabinet, reaffirmed Tehran's support for Iraq's territorial unity and its fight against militants.
"Abadi pointed to the presence of many dangers posed in the region as a result of the existence of the terrorist gang Islamic State, which requires regional and international efforts to exterminate this terrorist organisation," the Abadi's office said in a statement after the talks with Zarif.
Iran would continue to stand by Iraq, Zarif said.
"Iran backs the unity of Iraq and the stabilising of security and considers that as a priority in its foreign policy," he said.
Iran and Iraq fought an eight-year war in the 1980s, but Shi'ite Tehran forged close ties with the Shi'ite-led governments that have dominated Iraq since the overthrow of Saddam Hussein in 2003.
The advance of Islamic State through northern Iraq has alarmed the Baghdad government and its Western allies, prompting the first U.S. air strikes in Iraq since U.S. occupation forces pulled out in 2011.
In Washington, Republicans called for more aggressive U.S. action to defeat Islamic State, accusing President Barack Obama of policies that have failed to thwart potential new threats on U.S. soil.
Representative Mike Rogers, Republican chairman of the House of Representative Intelligence Committee, urged the administration to work with Arab partners on robust steps to disrupt the operations of Islamic State. He said the group is drawing support from Europeans and Americans who could travel undetected to Western countries to carry out attacks.
"They are one plane ticket away from U.S. shores," Rogers said on NBC's "Meet the Press".
The horrific video showing the killing of Foley last week, together with a threat to kill another American journalist being held hostage, Steven Sotloff, inspired widespread revulsion in the West and a desire to hunt down the killer.
The masked knifeman shown in the video spoke English with a London accent and security services have launched a major attempt to find out who he is by analysing the video and seeking to identify him from among the estimated 500 Britons believed to have gone to join the jihadists in Iraq and Syria.
Britain's ambassador to the United States, Peter Westmacott, told CNN's "State of the Union" programme that Britain was putting a great deal of resource into identifying the suspect, including voice-recognition technology.
He said he could not give more details, but added: "I do know from my colleagues at home that we are close."
Former hostages of Islamic State have suggested that the man in the video is one of a group of British Islamists assigned to guard foreign prisoners. They have been dubbed John, Paul and Ringo, of the Beatles, because of their British accents, and British media say the suspect is "jihadi John".
A U.S. journalist missing since 2012 was meanwhile freed by kidnappers in Syria on Sunday following efforts by Qatar to win his release, al Jazeera reported.
The Qatari-owned television station named the journalist as Peter Theo Curtis, and said he had been handed over to a representative of the United Nations.
The British government said it had appointed its senior defence adviser for the Middle East as a security envoy to the Iraqi Kurdistan to help Kurdish and Iraqi efforts to defeat Islamic State.
Lieutenant General Sir Simon Mayall goes to Baghdad and Arbil next week.
The government also said it would supply non-lethal equipment to Kurdish forces in the coming days, including night vision equipment and body armour.
Islamic State militants have mostly routed Kurdish forces in the north in recent weeks, seizing more towns, oilfields and Iraq's largest dam. Backed by U.S. air power, Kurdish forces later took back control of Mosul dam.
Islamic State has also seized large areas of Syria, declaring an Islamic Caliphate that crosses the national border.
Islamic State militants stormed an air base in northeast Syria on Sunday, capturing most of it from government forces after days of fighting, a witness and a monitoring group said.
Fighting raged inside the Tabqa air base, the Syrian army's last foothold in an area otherwise controlled by Islamic State.
In nearby Raqqa city, Islamic State's main stronghold, there was celebratory gunfire and several mosques announced through their loudspeakers that the base had fallen to Islamic State and cheered "God is greatest", a witness told Reuters.
Syrian state television said that after fighting fierce battles, the military was regrouping its forces and continuing to strike what it called terrorist groups.
Bombings across Iraq killed at least 35 people on Saturday in apparent revenge attacks after Shi'ite militiamen machine-gunned a Sunni Muslim mosque in Diyala province on Friday, killing 68 worshippers and deepening the country's sectarian conflict.
The violence continued on Sunday, when a car bomb killed seven people in a mostly Shi'ite area of Baghdad, police and medical sources said. (Additional reporting by Michael Georgy in Baghdad and Sylvia Westall in Beirut; Writing by Giles Elgood; editing by Anna Willard)