* Falluja, near Baghdad, in IS hands for two years
* Iraq, U.S.-led coalition not disclosing plans for Falluja
* Kurds say Falluja should be taken before Mosul (Adds comments from militia official, analyst)
By Ahmed Rasheed and Stephen Kalin
BAGHDAD, Dec 31 (Reuters) - Iraqi forces may face a big battle near Baghdad before they can try to retake the Islamic State stronghold of Mosul: Falluja, a long-time bastion of Sunni Muslim jihadists at the capital's western gates.
Prime Minister Haider al-Abadi's government and the U.S.-led coalition backing it have been cagey so far in plans for Falluja, which lies between Baghdad and Ramadi, the capital of western Anbar province that the Iraqi military recaptured this week from the militants.
Falluja was the first Iraqi city to fall to Islamic State in January 2014, six months before the group that emerged from al Qaeda swept through large parts of Iraq and neighbouring Syria.
Abadi said on Monday the army would head next to Mosul, the biggest urban centre under Islamic State control. He said its capture would mark the end of the "caliphate" proclaimed from the northern city's main mosque in June 2014.
But with many western and northern areas still held by Islamic State, the authorities have not made clear what path they intend to take to Mosul, 400 km (250 miles) north of Baghdad.
"The government will need to control Falluja before Mosul," Jabbar al-Yawar, secretary-general of the peshmerga - the forces of the Kurdish regional government fighting Islamic State in northern Iraq - told al-Hadath TV.
Ahmed al-Assadi, a spokesman for the Hashid Shaabi - a coalition of mostly Iranian-backed Shi'ite militias set up to fight Islamic State - said Falluja would likely come before Mosul. "But the final decision is with the commander-in-chief," he added, referring to Abadi, to whom the Hashid formally report.
Daily military statements mention air strikes and attacks by the Iraqi army and the international coalition in and around Falluja, a city with a pre-war population of around 300,000 located 70 km (45 miles) west of the capital.
But there has been no indication of if and when a battle will be launched to take the city, which Baghdad-based analyst Hisham al-Hashimi said contains around 1,000 Islamic State fighters.
"There's a military leadership; there's planning and a military vision," Brigadier-General Yahya Rasool, spokesman for the joint operations command told Reuters on Thursday. "If a battle starts to liberate the centre of Falluja, Falluja itself or any other area, we will announce it officially."
About 3,000 families remaining in Falluja could be used as human shields, said Hashimi, who has worked with the Iraqi government.
Around 70,000 families have taken refuge around Baghdad, according to Iraq's High Commission for Human Rights.
Falluja, downstream from Ramadi in the Euphrates River valley, is encircled by Iraqi forces, according to the international coalition, though some militants manage to slip past the cordon.
Assadi said the Hashid were present south of Falluja, on the road leading to the Shi'ite shrine city of Kerbala, as well as in some eastern and western areas. There they had helped to isolate the city and hold areas, freeing up the military to advance.
Maria Fantappie, Iraq analyst at the International Crisis Group, said that despite Falluja's proximity to Baghdad, it was not necessarily the next target.
Ramadi's strong tribal networks had made it easier for Iraqi forces to forge alliances and take control of key areas. "Falluja has more of an urban structure where tribes are present but are less a structuring element of the city, so it's going to be much harder to retake and keep the city under control," she said from Istanbul.
Known as the "City of Minarets and Mother of Mosques", Falluja is a focus for Sunni faith and identity in Iraq. It was badly damaged in two offensives by U.S. forces against al Qaeda insurgents in 2004.
The tribes of Anbar helped turn the tide of that insurgency at its height in 2006, banding together and making common cause with U.S. troops to rout al Qaeda.
The group's resurgence as Islamic State has divided residents of Anbar, where many accuse former Prime Minister Nuri al-Maliki of shutting Sunnis out of power and being a pawn of Shi'ite power Iran. Some support the Islamist militants, or are too fearful to move against them.
Fantappie said any attempt to retake Falluja could face local resistance because of a deal struck more than two years ago between the jihadis and the city's tribal and urban elements.
Yet local government officials said the capture of Ramadi, the largest Sunni city regained from Islamic State, had weakened the militants' morale. It had also created tension with Falluja residents as well as provoking clashes with Sunni tribes. Those reports could not be independently confirmed.
"After some Daesh fighters fled Ramadi to Falluja ... fears mounted among Falluja residents that a government offensive on their city could be imminent and pushed many families to try to leave the city," said Ibrahim al-Fahdawi, a member of the city council, using a derogatory Arabic acronym for the militants.
"Daesh elements threatened to execute anyone trying to flee, which triggered a squabble that developed into clashes between residents and Daesh, who were mostly foreigners," he told Reuters by phone.
(Additional reporting by Saif Hameed; Writing by Maher Chmaytelli; Editing by Giles Elgood and David Stamp)
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