The announcement came amid a Palestinian report that the two Palestinian factions are holding secret reconciliation talks.
"The (Hamas) government will allow all Fatah members who are from Gaza and who left the Strip (in 2007) to return, without any preconditions," apart from those accused of killing Hamas members during intense factional fighting that year, Haniya said.
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Speaking to reporters after a visit to the Hamas interior ministry in Gaza City, he added the authorities would "release a small number of Fatah members who are imprisoned (in Gaza) for security reasons."
Fatah MPs, who are based in the West Bank, would also be allowed to visit Gaza, Haniya added.
Fatah's spokesman brushed off Hamas's gesture. "What the Palestinian people really want is a genuine end to the division. They want unity, the formation of a government, lifting Hamas's veto on national elections and carrying through on what it agreed on in the past," Ahmed Assaf told Reuters.
Hamas' announcement came as Palestinian news agency Ma'an reported that Hamas and Fatah have secretly resumed reconciliation talks in an attempt to finalize an agreement.
Assaf, the Fatah spokesperson, said in a statement received by Ma'an that Fatah official Azzam al-Ahmad, who is in charge of reconciliation talks, spoke on Sunday with his Hamas counterpart Mousa Abu Marzouq.
The two followed up on discussions that began in Doha between al-Ahmad and Hamas chief-in-exile Khalid Mashaal, Ma'an reported.
Our hearts are openAssaf's statement emerged following news reports claiming that Hamas and Fatah have already reached agreement on a unity government. He made it clear that no agreement had yet been reached as of yet, while stressing that efforts are ongoing.
"Our hearts are open and our hands are extended for national unity," Ma'an quoted him as saying.
Acording to the AFP, Hamas has reached out to Fatah in recent months as Israel and Egypt have tightened their blockade on Gaza. Haniya spoke via telephone to Fatah leader and Palestinian president Mahmud Abbas in October, stressing the need for reconciliation and "a return to national unity."
Longtime tensions between Hamas and Fatah boiled over in a week of fighting in 2007 that left the Islamist movement – which is sworn to Israel's destruction – in charge of the impoverished coastal Gaza Strip.
The fighting came a year and half after Hamas won a landslide victory in Palestinian general elections, leading to a Western boycott of the Islamist-run government. Since the takeover both movements have launched tit-for-tat crackdowns on their rivals in the areas under their control.
The two sides have made repeated attempts to heal the rift, most recently by signing an Egyptian-brokered deal in 2011 in which they pledged to set up an interim government of independents to pave the way for new elections.
The agreement has never been implemented.
The Islamist movement says it has been under severe pressure since the Egyptian army destroyed hundreds of tunnels used to smuggle fuel and goods into the blockaded Gaza Strip following its overthrow of president Mohammed Morsi. Hamas is the Palestinian branch of Egypt's Muslim Brotherhood, from which Morsi hails.