The offices were attacked yesterday after Chechen leader Ramzan Kadyrov accused Beeline and another Russian mobile operator, Megafon, of rigging a vote to prevent a mosque in Chechnya's main city Grozny from being named Russia's most popular landmark.
Amateur video posted on YouTube showed dozens of young men in Grozny pelting a Beeline office and a building with a Megafon sign with eggs and other objects, shouting "Shame!", with the sound of breaking glass clearly audible.
Aibasheva said all ten offices reopened on Saturday morning, but that services in Chechnya remained disrupted after a fibre optic cable was ruptured yesterday.
The Grozny mosque, built in 2008 and known as the "heart of Chechnya", took an early lead in the online contest, overtaking better-known attractions including Baikal, the world's deepest lake, Peter the Great's Peterhof palace in Saint Petersburg, and the Solovetsky monastery in the Far North.
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By yesterday the mosque had over 38 million votes after Kadyrov, the region's controversial leader, urged people to support it online or by text message.
Kadyrov said on his Instagram blog that Chechens were switching to Chechen-based Vainakh Telecom phone provider.
"We are not planning to continue to feed Megafon and Beeline," he wrote. "The Heart of Chechnya is a symbol of Russia, a symbol of the whole world."
Over the past 20 years, Moscow has fought two separatist wars in Chechnya, the region that has been ruled by Kadyrov with an iron fist since 2007.
Kadyrov, a former rebel leader turned Kremlin supporter, has sought to draw publicity for Chechnya with massive projects like the Grozny mosque.