Plans by Macias to return to the North African nation in 2000 and 2007 were canceled because of protests, al-Arabiya said.
"Nobody banned Macias from entering the country in which he was born and raised," Mehal said in an interview with Radio Orient quoted by al-Arabiya. "All French citizens are welcome in Algeria and this includes Macias."
The decision to invite the singer, whose brother fought for the French during Algeria's war for independence, sparked harsh criticism, al-Arabiya said. Political analyst Abdul Aali Razaki told the network Algerians "are known for their dislike of all things Jewish."
The Algerian activist known as Algerie Salah de Londre posted a video on YouTube slamming Mehal's invitation, saying it is not because Macias is Jewish that Algerians protest, but because of the singer's support for Israel.
Mehal said Macias had planned to visit Algeria in 2000 but changed his mind after Algerians staged street protests, demanding he be banned from the country. In 2007, former French President Nicolas Sarkozy included Macias in his official delegation for a visit to Algeria but the singer declined after then-Algerian Prime Minister Abdel Aziz Belkhadem threatened to boycott the Sarkozy's visit, al-Arabiya said.