The Tunisian transport ministry said in a statement earlier that Emirates flights would be suspended until the UAE airline found a way to operate according to worldwide law and treaties.
They urged the UAE authorities to learn from Tunisia's experience in promoting equality and respect for the rights of all genders.
"Based on the higher travel advisory restriction issued by the United Arab Emirates government, airlines are instructed that all Tunisian female nationals will be denied entry to the UAE by API-UAE", read an internal Emirates Airline email.
That triggered angry reactions on social media and media outlets in Tunisia.
Emirates said on Twitter it would stop its Dubai-Tunis connection from Monday following instructions from Tunisia.
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"We should avoid misleading attempts at misinterpretation and misrepresentation", Dr Gargash said.
Officials in Tunis have barred the carrier from touching down in the capital due after the airline stopped the country's women from flying to or transiting through the UAE at the weekend.
The Tunisian president's spokeswoman, Saidra Qrash, said that security agencies in some countries have warned recently that a number of Tunisian women, or women who carry Tunisian passports, have returned from Syria and Iraq where they had fought with ISIS, reported Gulf News. The close ties between Tunisia and Qatar as well as the existence of Muslim brotherhood in Tunisia are all issues that put Tunis and Abu Dhabi at loggerheads, especially at times when the UAE gears its foreign policy to countering political Islam at home and overseas.
Tunisia had expressed its understanding of the UAE concerns, he said.