Last week Egyptian and Libyan warplanes hit IS targets inside Libya after the jihadists released a video on February 15 showing the beheadings of 21 Christians, most of them Egyptian.
Since then Egypt has urged the hundreds of thousands of Egyptians who work in Libya to leave, and also chartered planes to ferry many of them home from Tunisia, which also shares borders with Libya.
At least 14,585 Egyptians have heeded that call and returned home crossing from the Sallum border post in northwest Egypt, state news agency MENA reported.
A Tunisian transport ministry spokeswoman meanwhile said that at least 1,000 Egyptians who had fled Libya have been airlifted home from her country on planes chartered by Cairo since Friday.
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She told AFP that 250 more Egyptians were expected to leave from the southeastern Djerba-Zarzis airport by 1600 GMT.
A Tunisian customs official said that an unspecified number of Egyptians were also waiting on the Libyan side of the border, hoping to cross the frontier.
In July last year, thousands of Egyptians fleeing violence in Libya were stranded for days at the border with Tunisia, as authorities refused to let them in until Cairo had arranged for their transport home.
Days after the revolt erupted, Egypt had sent military planes to Libya to evacuate up it citizens trapped in the violence.
At the time, officials said 1.5 million Egyptians worked in Libya, mostly in the construction and services industries, and formed the backbone of the expatriate workforce in the oil-rich nation.
Hours after IS released the video showing the beheading of the Coptic Christians, Egypt carried out air strikes on IS targets inside Libya.