"(Twitter) has announced that it is prepared to negotiate to resolve problems," Mohammad-Javad Azari Jahromi told the Iran daily newspaper.
"Considering the current situation there are grounds for such negotiation and interaction. Twitter is not an immoral environment needing to be blocked," he added.
The 36-year-old Jahromi became Iran's youngest-ever minister this week, and the first to be born after the 1979 Islamic revolution.
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His selection has been criticised by rights groups over his involvement in surveillance during and after the mass anti-regime protests of 2009.
But Jahromi is also seen as a critic of online censorship in Iran, where sites such as Facebook, YouTube and Twitter remain banned even if millions use them daily through easily available privacy software.
There was no immediate response from Twitter to his comments.
He said officials were also looking at ways to unblock YouTube while still censoring "immoral content" on the site, and that a pilot project was being run, allowing universities to access the site.
Jahromi added that the final decision on unblocking Twitter did not lie with his ministry, but with the Supreme Council for Cyberspace, which includes members of the hardline judiciary.
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Twitter was banned at the time of mass anti-regime protests in 2009, that followed allegations of massive rigging in the re-election of president Mahmoud Ahmadinejad.
But despite the ban, the US messaging service is widely used by supreme leader Ayatollah Ali Khamenei, who has official accounts in several languages, as well as President Hassan Rouhani and Foreign Minister Mohammad Javad Zarif.
Even Ahmadinejad joined the service this year.
Separately, Jahromi rejected allegations he was involved in interrogations during the 2009 protests.
"I wasn't responsible for surveillance -- I was in charge of the technical infrastructure for the surveillance industry, and I consider it an honour," he said in a meeting with lawmakers this week, according to the Shahrvand newspaper.
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