Gaza's Hamas rulers executed three Palestinians convicted of murder on Tuesday, sparking criticism from human rights groups and defying an agreement with the rival Palestinian Fatah faction.

The executions, which were carried out without the required approval of Palestinian President Mahmoud Abbas, marked the first time the Islamic militant group applied the death penalty since a Hamas-Fatah unity government was formed in 2014.

Hamas violently routed Abbas' Fatah forces from Gaza in 2007 and the factions have since unsuccessfully tried to reconcile.

Fatah spokesman Osama Qawasmi said the executions without Abbas' approval were "a crime, a clear violation of the law and a deepening of the split. It's a clear message from Hamas that it doesn't want national unity and it doesn't care about Palestinian law."

The 2014 unity government deal was never implemented. Hamas remains the de facto authority in Gaza, preventing the government from extending control over the coastal strip.

Gaza's Interior Ministry said the executions took place at the central prison after the victims' families rejected the possibility of a last-minute pardon. Two men were hanged and the third was killed by firing squad.

International and local rights groups had urged Hamas not to carry out the executions.

"No one should be put to death, certainly not as part of a legal system in which torture and coercion are common," said Sari Bashi from Human Rights Watch. She said Hamas was using the death penalty as a deterrent against a wave of crime in the Gaza Strip rather than addressing the issues that have led to that crime.

In a statement, the office of the U.N. High Commissioner for Human Rights, Zeid Ra'ad al-Hussein, condemned the executions.

During the 2014 war with Israel, Hamas extra-judicially killed 23 Palestinians suspected of spying for Israel.

Hamas has executed 22 people convicted of murder or collaboration since 2007.