Isis chief Abu Bakr al-Baghdadi called on the “soldiers of the Islamic state” to fight alongside his jihadist group, telling them: “If you have faith, you will conquer Rome.”
“The Islamic community sees our jihad with the eyes of hope,” al-Baghdadi was quoted by Rai News as saying.
The report comes just days after the Isis leader declared the establishment of a "caliphate", or Islamist state, in Syria and Iraq. According to a map published online, the plans also envisage expansion of the Islamic state into Europe and across Africa, Asia and the Middle East.
In an audio recording released online on Sunday, Isis declared al-Baghdadi "the caliph" and "leader for Muslims everywhere".
The jihadists said their caliphate would spread from Aleppo in northern Syria to Diyala in eastern Iraq, and ordered Muslims in those areas to "obey" and pay allegiance to their new leader.
"The Shura [council] of the Islamic State met and discussed this issue...[and] the Islamic State decided to establish an Islamic caliphate and to designate a caliph for the state of the Muslims," said Isis spokesman Abu Mohammad al-Adnani.
"The jihadist cleric Baghdadi was designated the caliph of the Muslims," said Adnani, adding that the caliphate would extend "from Aleppo [in northern Syria] to Diyala" in Iraq.
Baghdadi "has accepted this allegiance, and has thus become the leader for Muslims everywhere" and is to be known hereof as "Caliph Ibrahim" - a reference to his real name.
"The words 'Iraq' and 'the Levant' have been removed from the name of the Islamic State in official papers and documents," Adnani said.
The caliphate is "the dream in all the Muslims' hearts" and "the hope of all jihadists", he said.
Ever since the Prophet Mohammed's death, a caliph was designated "the prince" or emir "of the believers".
After the first four caliphs who succeeded Mohammed, the caliphate lived its golden age in the Omayyad empire from the year 661 to 750, and then under the Abbasids, from 750 to 1517.
It was abolished when the Ottoman empire collapsed in 1924.
In the recording, Adnani demanded that all Muslims "pledge allegiance" to the new leader and "reject democracy...and other garbage from the West" saying "the West and the East will submit to you".
"Today the unfaithful are angry...today the unfaithful countries of the West are trembling."
Celebrations in Syria stronghold
An activist in Raqa, the bastion of Isis, told AFP via the internet: "Large convoys of Isis members arrived in the city just as the declaration was issued, to celebrate their caliphate.
"There was very intense gunfire. Isis supporters were shooting in the air with joy," Hadi Salameh said.
"I even saw seven Isis members come into Raqa on horseback."
Another activist, Abu Ibrahim, said via Facebook: "Isis members in Al-Naim Square [in Raqa] are calling on all residents to pledge their loyalty."
Opposed to Isis, both Salameh and Abu Ibrahim said they feared the consequences of the declaration.
"More jihadists will be drawn to join Isis, and they will become stronger. It's crazy," said Abu Ibrahim.
In Syria, Isis' fighters control large swathes of territory in Deir Ezzor near the Iraq border, Raqa in the north, as well as parts of neighbouring Aleppo province.
In Iraq, it has spearheaded a lightning offensive in recent weeks, capturing sizeable territories in the north and west of the conflict-torn country.
Once welcomed in Syria by rebels seeking President Bashar al-Assad's ouster, Isis quickly earned the wrath of the Syrian opposition because of its systematic abuses.
On a near-daily basis, reports have emerged of Isis jihadists summarily executing political and military rivals, as well as average civilians.
It has kidnapped thousands of people, including many rebels seeking Assad's overthrow.