"Hamas invites the consensus government to come to Gaza to practice its mission and carry out its duties in the Gaza Strip immediately, and it accepts holding general elections," Hamas said in the statement.
The decision was in response to reconciliation talks between the principal Palestinian factions, Hamas and Fattah, mediated by Egypt. The two sides were still in the Egyptian capital of Cairo on Sunday night.
Hamas ousted the Fatah-dominated Palestinian Authority from Gaza in 2007 and Fatah continued to oversee the West Bank.
They failed to implement reconciliation agreements aimed at creating one shared government.
"This puts Abu Mazen and Fatah to the real test," Hamas spokesman Fawzi Barhoum said in a statement on Hamas' official website. "Our people is looking for a practical and actual response to achieve its ambitions of national unity and real partnership."
Hamas wants Palestinian President Mahmoud Abbas to lift punitive measures against Hamas in Gaza over the past four to five months, including budget cuts to Gaza for electricity, medical services, salaries.
"If the news is correct, that is good and positive," Fatah Vice Chairman Mahmoud al-Aloul said in a statement posted on Fatah's official Facebook page. "But we do not want to act with haste regarding what is being said in the news."
Abbas is to meet U.S. President Donald Trump on Wednesday, before his speech at the United Nations on Thursday.
Abbas has viewed Hamas' control as a shadow government and called for the dissolution of Hamas' administration.
Hamas is in a weak strategic position, according to Kobi Michael, the former head of the Palestinian desk at Israel's Ministry for Strategic Affairs.
"They're ready to go down on their knees and to reconcile with the Egyptians," Michael said in a conference call with Bloomberg. "We are witnessing a sort of institutionalization process in which Hamas goes from being a terrorist organization and semi-state actor to being a state actor." It is one that "is still very hostile and dangerous toward Israel."
He said this is a positive sign for Israel, which borders Gaza.