A day earlier, Abbas ordered his Fatah-dominated security services in the West Bank to release all pro-Hamas activists, according to the official Palestinian WAFA news agency. Hamas said the activists had not yet been freed.
Hamas security men detained Ibrahim Abu an-Naja and Zakaria al-Agha, who were appointed by Abbas to oversee Fatah in the Gaza Strip after Hamas Islamists seized control a year ago, Fatah officials said.
Hamas forces also arrested three local governors appointed by Abbas, whose West Bank-based government is backed by the United States and other Western powers.
Hamas leader Sami Abu Zuhri said the arrests in the Gaza Strip were meant to put pressure on Abbas' security forces to release Hamas activists detained in the occupied West Bank.
He accused Abbas' forces of trying to "liquidate" Hamas and described the Gaza arrests as "temporary and limited".
Despite Abbas's order on Thursday, Abu Zuhri said none of the Hamas men have been freed. "When political arrests end in the West Bank, everything else will come to an end," he said.
Fatah official Abdallah Abdallah condemned the Gaza arrests, saying they "Constitute the destruction of any Palestinian and Arab call to end the schism" Between Hamas and Fatah.
Tensions between the factions spiked a week ago after a series of bombings in the Gaza Strip, one of which killed five Hamas members and a girl. Hamas blamed Fatah for the blasts, a charge Fatah denied.
Hundreds of Palestinians have since been arrested in week-long tit-for-tat crackdowns by Fatah in the West Bank and Hamas in the Gaza Strip.