Palestinian security forces have carried out their first executions since 2002, reversing a stay imposed in response to international pressure.
Mahmoud Abbas is under pressure to crack down on crime
Four men who had confessed to murders in a Gaza court were killed on Sunday - three by hanging, one by firing squad.
The executions are part of the Palestinian Authority's (PA) attempt to rein in lawlessness, a spokesman said.
The death penalty is likely to be opposed by the European Union, top donor to the PA, say correspondents.
Human rights groups had expressed their concern at the revival of the death penalty - indicated in February by Palestinian leader Mahmoud Abbas.
Mr Abbas signed the order on Saturday, interior ministry spokesman Tawfiq Abu Housa said.
"There is a new policy of enforcing the law to face and fight the chaos and lawlessness in the Palestinian territories," Mr Housa said.
Until Sunday, nine death sentences had been carried out since the formation of the Palestinian Authority in 1994 - out of 70 imposed by the courts, according to the Palestinian Centre for Human Rights.
Late leader Yasser Arafat stopped authorising executions in 2002 following international criticism of the measure.
In February, Mr Abbas - responding to pressure from Palestinians to end "security chaos" in the Gaza Strip - asked the Grand Mufti of Jerusalem, Sheikh Ikrima Sabri, for an Islamic legal ruling on the death penalty.
Sheikh Sabri was asked to review 51 cases - about half concerning alleged collaborators with Israel, an especially sensitive issue, correspondents say.
The grand mufti recommended a resumption of executions saying a delay of the execution orders "encouraged the phenomenon of revenge in the Palestinian community".