* Baghdadi calls for jihad, says Muslims wronged around world
* Urges believers to come to self-proclaimed caliphate (Adds quotes)
By Yara Bayoumy
DUBAI, July 1 (Reuters) - The leader of the al Qaeda offshoot that has taken control of parts of Iraq and Syria has urged Muslims around the world to fight to avenge wrongs committed against their religion.
Abu Bakr al-Baghdadi, head of the group that now calls itself the Islamic State, issued the call to jihad - holy war - in an audio message lasting nearly 20 minutes that was posted online on Tuesday.
It was his first purported message since the group - previously known as the Islamic State in Iraq and the Levant (ISIL) - proclaimed a 'caliphate' on the territory it has captured.
Baghdadi named a string of countries, from Central African Republic to Myanmar (Burma), where he said violations were being committed against Muslims.
"Your brothers, on every piece of this earth, are waiting for you to rescue them," he said.
"By Allah, we will take revenge, by Allah we will take revenge, even if after a while," he said in the message that came on the third day of the Muslim holy month of Ramadan.
Fighters should "embrace the chance and champion Allah's religion through jihad", Baghdadi said.
He called on Muslims to immigrate to the self-styled "Islamic State", saying it was their duty.
On Sunday ISIL claimed universal authority throughout the Muslim world, declaring Baghdadi its caliph - a mediaeval title last widely recognised in the Ottoman sultan deposed 90 years ago, after World War One.
The move followed a three-week drive for territory by ISIL militants and their allies among Iraqi's Sunni Muslim minority. The caliphate aims to erase colonial-era borders and defy the U.S.- and Iranian-backed government of Shi'ite Prime Minister Nuri al-Maliki in Baghdad.
It also poses a direct challenge to the global leadership of al Qaeda, which has disowned ISIL, and to conservative Gulf Arab Sunni rulers, who already view the group as a security threat.
Earlier on Tuesday, Shi'ites failed to name a prime minister to replace Nuri al-Maliki at the first meeting of a new parliament session, dashing hopes that a unity government would be swiftly built to save Iraq from collapse. (Additional reporting by Ali Abdelaty in Cairo, Amena Bakr in Doha and Dominic Evans in Beirut; Writing by Yara Bayoumy; Editing by Mark Trevelyan)