The group, which seized control of the coastal territory in 2007, executed on Thursday two Palestinians convicted of helping Israel track and kill militants in Gaza.
The execution sparked a major outcry among Palestinian rights groups and international organizations like Amnesty International and Human Rights Watch. The United Nations called for a halt to the practice and France condemned it as murder.
"We will continue to implement execution sentences," Fathi Hammad, minister of interior in Hamas's Gaza-based government, told reporters.
Hammad said capital sentences would also be handed out for serious criminal offenses, such as murder and major drugs crimes.
Thursday's execution by firing squad was carried out in defiance of Western-backed President Mahmoud Abbas, who formed a new administration in the West Bank after being expelled from Gaza by Hamas about three years ago.
Under Palestinian law, the president has the final say in the implementation of capital sentences, but neither Hamas nor Abbas's Fatah faction recognize the legitimacy of the other.
Hamas has opposed Abbas's peace moves with Israel and refuses to recognize the Zionist state.
Since it formed its first government in 1996, the Palestinian Authority has executed several Palestinians who were either charged with murder or with working for Israel. The last such execution took place in 2005.
Amnesty International's Middle East director, Hassiba Hadj Sahraoui, said her group was concerned for other Palestinian prisoners in Gaza who have been given death sentences by Hamas military courts.
"We deplore that these men were convicted in unfair military proceedings," said Sahraoui.
