* Battles continue around Tikrit
* Group rebrands as cross-border state
* Fighters have won land in Iraq and Syria
* Combatants accused of brutal violence
* Declaration could cause infighting with other rebels
By Oliver Holmes and Isra'a al-Rubei'i
BAGHDAD, June 30 (Reuters) - Iraqi troops battled to dislodge an al Qaeda splinter group from the city of Tikrit on Monday after its leader was declared caliph of a new Islamic state in lands seized this month across a swathe of Iraq and Syria.
Alarming regional and world powers, the Islamic State in Iraq and the Levant (ISIL) claimed universal authority when it dropped the local element in its name and said its leader Abu Bakr al-Baghdadi, as leader of the Islamic State, was now caliph of the Muslim world - a mediaeval title last widely recognised in the Ottoman sultan deposed 90 years ago after World War One.
"He is the imam and caliph for Muslims everywhere," group spokesman Abu Muhammad al-Adnani said in an online statement on Sunday, using titles that carry religious and civil power.
The move, which follows a three-week drive for territory by ISIL militants and allies among Iraqi's Sunni Muslim minority, aims to erase international borders drawn by colonial powers and defy Baghdad's U.S.- and Iranian-backed, Shi'ite-led government.
It also poses a direct challenge to the global leadership of al Qaeda, which has disowned it, and to conservative Gulf Arab Sunni rulers who already view the group as a security threat.
Fighters from the group overran the Iraqi city of Mosul on June 10 and have advanced toward Baghdad, prompting the despatch of U.S. military advisers. In Syria, ISIL has captured territory in the north and east, along the desert frontier with Iraq.
The government of Prime Minister Nuri al-Maliki, with the help of Shi'ite sectarian militia, has managed to stop the militants from reaching the capital but security forces have been unable to take back cities they abandoned in the fighting.
The army attempted last week to take back the city of Tikrit but was unable to seize the city. Helicopters hit Islamic State positions around the city overnight. On the southern outskirts, a battle raged into Monday, residents in the areas said.
Tikrit was the home city of Saddam Hussein, whose overthrow by U.S. forces in 2003 ended a long history of domination by Sunnis over what is today a Shi'ite majority in Iraq.
The fighting has started to draw in international support for Baghdad, two and a half years after U.S. troops pulled out.
Armed and trained by the United States, Iraq's armed forces crumbled in the face of the ISIL onslaught and have struggled to bring heavier weaponry to bear. Only two aircraft - turboprop Cessna Caravans normally used as short-range passenger and cargo carriers - are capable of firing the powerful Hellfire missile.
The U.S. is flying armed and unarmed aircraft in Iraq's airspace but says it has not engaged in fighting.
Russia has sent its first warplanes to Baghdad, filling an order for five second-hand Sukhois. The government said they will be operational within a few days.
In Falluja, just west of Baghdad where Islamic State fighters have been in control for six months, a bank accountant who asked to remain anonymous for fear of retribution said the announcement of the caliphate was a "step backward".
"It will only turn the government even more hostile to us," he said. "This will isolate us further from the rest of the world."
The Islamic State has used alliances with other, less radical Sunni armed groups and tribal fighters who are disillusioned with Maliki. Members Saddam's secular Baath party have also fought in the revolt.
The Sunni Muslim militant group follows al Qaeda's hardline ideology, viewing Shi'ites as heretics.
Its declaration of the Islamic State could isolate allies in Iraq and lead to in-fighting. Such internal conflicts among rebel groups in Syria has killed around 7,000 people there this year and complicated the three-year uprising against Syrian President Bashar al-Assad, another ally of Shi'ite Tehran.
The group crucified eight rival rebel fighters in Syria, a monitoring group said on Sunday. And in the Syrian city of Raqqa, controlled by the Islamic State, militants held a parade to celebrate the declaration of the caliphate.
The Islamic State posted pictures online on Sunday of people waving black flags from cars and holding guns in the air, the SITE monitoring service said.
Some analysts say the group is a credible threat to frontiers and is stirring regional violence while others say it exaggerates its reach and support through sophisticated media campaigns.
The Islamic State also released a video called "Breaking of the Borders", promoting its destruction of a frontier crossing between the northern province of al-Hasakah in Syria and Nineveh province in Iraq, said SITE, which tracks militant websites.
(Additional reporting Sylvia Westall in Beirut; Editing by Alastair Macdonald)