The jihadist group has said it was behind a suicide bombing in the centre of Tunis on Tuesday in which 12 presidential guards died.
IS also claimed two attacks earlier this year at the National Bardo Museum in Tunis and on a hotel near the Mediterranean resort of Sousse that killed a total of 60 people, all but one of them foreign tourists.
"Everything is being planned in Libya," Tunisia's secretary of state for national security, Rafik Chelly, told private Mosaique FM radio.
IS, which controls swathes of Syria and Iraq, has exploited the chaos that spread across oil-rich Libya after veteran leader Moamer Kadhafi was toppled and killed in the 2011 revolution.
"Libya has become a danger. That's why we have to take precautions... Audacious decisions," said Chelly.
British Foreign Secretary Philip Hammond acknowledged that Libya posed a "threat", during a visit Friday to Tunis where he met his Tunisian counterpart Taieb Baccouche and other officials.
"Your minister mentioned the challenges in your neighbour Libya and we are acutely conscious of the threat that your country faces from what's going on in Libya," he said after meeting Baccouche.
Thirty Britons were among the 38 tourists killed in the hotel attack near Sousse and on Friday Hammond attended a ceremony to commemorate the attack and visited the Bardo museum.
Tunisia announced on Wednesday it was closing its land border with Libya for 15 days, with Chelly saying the measure was "temporary" to give authorities time to mull what they should do next.
Tunisia has already built trenches and other obstacles along more than 200 kilometres (124 miles) of the 500-long border with Libya and will also reinforce land and sea surveillance, according to Chelly.
Prime Minister Habib Essid has told parliament that some materials used in Tuesday's attack were not available in Tunisia but can be found across the frontier in Libya.
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