The Hamas Minster of Transportation Osama Al-Aisawi said in a press statement that his government decided to name the squares after Dalal Al-Moghrabi, the Fatah woman who led the 1978 coastal mission in which 37 Israelis and an American photographer were killed, and Reem Al-Riyashi, a Hamas woman who carried out an attack in January 2004 at the Erez crossing in Gaza which killed four Israeli soldiers.
Aisawi said that the Cabinet took the decision to ensure that their names enters Palestinian history and to prove its independence from Fatah.
The minister was referring to an announcement on Thursday from the Palestinian Authority (PA), which had postponed the inauguration of a square named after Al-Moghrabi in Ramallah's Um Al-Sharayit neighborhood.
Hamas said that the PA's decision was the result of Israeli and American pressure.
The PA Ministry of Information had condemned Israel for attempting to prevent the inauguration.
A West Bank-based Hamas official told Arab News that the idea of constructing the Al-Moghrabi square and its financing was under the control of the Al-Biereh municipality, which is led by the movement.
"Unfortunately, the Fatah movement rejected our approach, which aimed to show the world that Palestinians are proud of their history and heritage,” the official said.
"Why does the PA postpone the inauguration of the square while the Israeli prime minister honors some (rightist Israeli) murderers and terrorists?"
The official attacked Fatah for abandoning its martyrs, claiming that Hamas is committed to honoring them. 
Spokesman for the PA’s security forces Adnan Al-Damiri said that the official ceremony to name the square after Al-Moghrabi was postponed for "technical reasons" and was not related to pressure from Israel and the US.
"No one in the world can prevent the Palestinians from being proud of their history and heritage. This history and heritage is part of our life," he said.
Hamas has been at odds with Palestinian President Mahmoud Abbas and the Fayyad government since the group forced pro-Abbas forces out of Gaza in deadly clashes in June 2007.