They discussed "the danger of terrorism and the importance of uniting efforts of all countries to fight it", SANA said.
Messahel's mission to Damascus follows Syrian Foreign Minister Walid Muallem's visit to Algeria in late March.
Algeria has systematically abstained in Arab League votes slapping sanctions on the Assad regime.
Syria was suspended from the pan-Arab body in 2011 over its brutal response to anti-government protests that escalated into a multi-sided conflict that has killed more than 270,000 people.
Assad has compared his country's war against rebels to the conflict between security forces and Islamist militants that devastated Algeria during the 1990s.
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Messahel's mission to Damascus follows Syrian Foreign Minister Walid Muallem's visit to Algeria in late March.
Algeria has systematically abstained in Arab League votes slapping sanctions on the Assad regime.
Syria was suspended from the pan-Arab body in 2011 over its brutal response to anti-government protests that escalated into a multi-sided conflict that has killed more than 270,000 people.
Assad has compared his country's war against rebels to the conflict between security forces and Islamist militants that devastated Algeria during the 1990s.
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