BAGHDAD, July 5 (Reuters) - Iraqi Shi'ite fighters and army troops made gains north of Falluja on Sunday but their efforts to seal off Islamic State militants in the city met heavy resistance, including suicide bomb attacks, army sources and militia fighters said. Prime Minister Haider al-Abadi's government is trying to reverse recent gains by Islamic State hardliners in the western province of Anbar after they seized the provincial capital Ramadi in May. Falluja, just 40 km (25 miles) west of Baghdad, was a center of Sunni Muslim armed opposition to the Shi'ite-led government even before Islamic State took control of most of Iraq's Sunni regions in June last year. Sunday's offensive was led by fighters from Kata'ib Hezbollah, part of the mainly Shi'ite Hashd Shaabi force fighting with the army against Islamic State. Spokesman Jaafar Hussaini said the group managed to cut off a supply line to Islamic State-held territory north of the city.