The micro-blogging platform was barred at the time of mass anti-regime protests in 2009 that followed allegations of massive rigging in the re-election of president Mahmoud Ahmadinejad.
"(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.
His selection has been criticised by rights groups over his involvement in surveillance during and after the mass anti-regime protests of 2009.
He rejected the criticism in a meeting with lawmakers this week, saying: "I wasn't responsible for surveillance -- I was in charge of the technical infrastructure for the surveillance industry, and I consider it an honour."
But Jahromi is also seen as a critic of online censorship in Iran, where platforms like Facebook, YouTube and Twitter remain banned even if millions use them daily through easily available privacy software.
He said officials were also looking at ways to unblock YouTube while still censoring "immoral content" on the video-sharing service, and that a pilot project would allow universities to access the site.
There was no immediate response from Twitter or YouTube.
Jahromi added that the final decision on unblocking sites lay with Supreme Council for Cyberspace, which includes members of the hardline judiciary.
Signup to our newsletter and follow us on Facebook and Twitter!
The 2009 protests were considered the first time that Twitter and social media were widely used to organise protests -- a model replicated when the Arab Spring movement erupted across the region the following year.
"At that time and based on remarks made by the director of this network, Iran's government believed they had interfered in the country's internal affairs and for this reason Twitter was filtered," said Jahromi, who has more than 4,000 followers on the service.
- 'Cyberspace can uproot religion' -
Despite the ban, Twitter 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.
But many conservatives remain worried about "Western infiltration" through social media.
In December 2016, Friday prayer leader Ayatollah Mohammad-Ali Movahedi Kermani, who heads the Committee for the Promoting Virtue and Prohibiting Vice, said the dangers of the internet were even greater than women failing to wear a headscarf.
"Bad hijab is a bad thing but cyberspace is a hundred times worse," he said in a speech to religious officials, highlighting the presence of porn and anti-religious sites.
"Cyberspace can uproot religion and Islam completely," he said.
Rouhani is thought to have favoured lifting the Twitter ban for some time, having even exchanged words with the site's co-founder Jack Dorsey back in 2013.
"Good evening, President. Are citizens of Iran able to read your tweets?" Dorsey posted shortly after Rouhani's first election win.
Rouhani replied: "Evening, @Jack... my efforts geared 2 ensure my ppl'll comfortably b able 2 access all info globally as is their #right."