Qatar has recalled its ambassador from Cairo after an Egyptian diplomat accused the Doha government of supporting terrorism in a dispute over Egyptian air strikes on Islamic State targets in Libya.

Egyptian warplanes bombed sites in Libya on Monday in response to the beheading of 21 Egyptian Christians by Islamic State militants there.

The Arab League expressed its "complete understanding" over the Egptian action and threw its weight behind Cairo's call for a lifting of the arms embargo on the Libyan army.

But at an Arab League meeting on Wednesday, Qatar said it had reservations over the attack.

Qatari foreign ministry official Saad bin Ali Al-Muhannadi said unilateral military action on another member could harm innocent civilians and would also give an advantage to one side in Libya's conflict, he said.

His comments drew swift condemnation from the Egyptian envoy to the league, Tareq Adel, who said they showed Doha "supports terrorism," according to the Egyptian news agency MENA.

Qatar's state news agency QNA reported later that Doha recalled its ambassador to Egypt for consultations. The developments revived a diplomatic row between the two countries following a recent improvement in relations.

The head of the Gulf Cooperation Council in turn rejected Tareq Adel's comments - indicating the council did not want to reopen an internal rift which peaked when Saudi Arabia, the United Arab Emirates and Bahrain withdrew their ambassadors from Doha last year over its support for Islamists.

"These accusations are baseless, distort the truth and ignore the sincere efforts Qatar has exerted with its GCC neighbours to combat terrorism and extremism on all its levels," GCC secretary-general Abdullatif bin Rashid Al-Zayani said.

But in a later statement, Zayani said the GCC continued to supported Egyptian President Abdel Fattah Al-Sisi, including over the military action taken in Libya.

Cairo accuses Qatar of supporting the Muslim Brotherhood, which was ousted from power in Egypt in 2013 when the army moved against the elected President Mohamed Mursi.

Saudi Arabia, the UAE and Kuwait have given Egypt billions of dollars in aid since Mursi was ousted.

Qatari Foreign Minister Khaled Al-Attiya, in an interview with the pan-Arab al-Hayat newspaper published on Thursday, said Doha did not support the Muslim Brotherhood.

Attiya said that there were "differences of opinion, which is healthy, and not disputes" between Gulf Arab countries. - Reuters