The statement reflects the view of the secretary of the League however it doesn't represent the official stance of the country members as noted in the article you posted.
“The statement issued... on behalf of the Arab League was not discussed with the League member-states before it was released”.
Who is the most powerful influential country in the Arab League after all ?
Saudi Arabia...
Quote :
Saudi king backs Turkish military action
Published: 09:46 August 3, 2015
Riyadh: Saudi King Salman has expressed support for Turkey after it launched air strikes against Daesh in Syria and Kurdish militants in Iraq, state media reported on Tuesday.
The king told President Recep Tayyip Erdogan on Monday that he backed Turkey’s right to self-defence, the official Saudi Press Agency said.
Erdogan had telephoned Salman to brief him on the air strikes it launched last week after a deadly bombing inside Turkey blamed on Daesh and a reprisal killing of police by Kurdish militants.
The king condemned the attacks and said he “supports Turkey’s right to defend itself and protect its citizens from terrorist acts” which pose a threat to the security of the region and the world, SPA said.
Saudi Arabia is part of a US-led coalition that has been carrying out air strikes against Daesh in Syria since last September.
But Turkey had previously stood aloof, prompting accusations - strongly denied by Ankara - of complicity with the terrorists.
Turkey and Saudi Arabia have had strained relations since 2013 when Riyadh supported the overthrow by the Egyptian army of Ankara-backed Islamist president Mohammad Mursi.
But SPA said the two leaders “emphasised the excellent relations” between their countries in their telephone call.
Saudi king backs Turkish military action | GulfNews.com
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