"The values of Islam oblige us not to take women, children, and the elderly as captives," said MK Mansour Abbas.
Elizabeth Tsurkov was kidnapped six months ago in Baghdad.
Lebanon's director general of public security accused Israel of involvement in the violence.
Rockets and bullets have fallen in areas outside of the refugee camp amid the clashes between Fatah and Islamist militants.
The "Muslim Youth" group reportedly stated that it was launching a battle to "purge the Ain al-Hilweh camp of apostates."
Islamic State on Monday claimed responsibility for the suicide bombing of a political rally in Pakistan that killed at least 45 people.
At least six people were killed in two days of clashes in a Palestinian refugee camp in Lebanon.
There are at least 40 confirmed casualties following an explosion in Pakistan's Khyber Pakhtunkhwa province.
Once Britain's most high-profile Islamist preacher, Choudary has been charged with three terrorism offenses after being arrested in London last week.
Court documents reveal that Al-Azhari, a US citizen who had spent a significant portion of his life abroad, adopted extremist Islamist/Salafist beliefs.
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