The UN envoy for the Middle East peace process, Nickolay Mladenov, said he had serious doubts as to whether capital trials there met fair trial standards.
Mr Mladenov added that he was disturbed by reports that some of the executions might be carried out in public.
One Palestinian group has documented 67 executions in Gaza since 2007.
However, that figure does not include the killings of people accused by Hamas of being collaborators during wartime. At least 25 were shot dead after the 2014 conflict with Israel.
Last week, Hamas-affiliated members of the Palestinian parliament announced they had approved a measure allowing executions to be carried out in Gaza without having first been ratified by Palestinian Authority President Mahmoud Abbas, who is based in the West Bank.
"We found it was important to implement the death penalty rule to maintain civil peace in society and to prevent cases of murder," Hamas MP Yehia Mousa told the New York Times.
It was not clear what authority the MPs had to authorize executions in the coastal territory, given that the full Palestinian Legislative Council has not met since Hamas reinforced its power in Gaza in 2007 following a violent rift with Mr Abbas' Fatah movement.
But the move came a week after Hamas leader Ismail Haniya said 13 Palestinians had been sentenced to death by courts in Gaza and would be executed as soon as possible.
Last month, the Palestinian Center for Human Rights (PCHR) said a military court had sentenced three men to death for collaborating with Israel.
That took the total number of death sentences issued so far this year in Gaza to 10, it added.
The Hamas authorities mostly stopped carrying out the death penalty in June 2014, when a government of national consensus was formed and officially placed in charge of Gaza.
However, that government never exercised authority there and, in July 2015, it was reshuffled without Hamas' inclusion or input.
In February, Hamas' military wing executed one of its commanders "for behavioral and moral violations".
Mahmoud Eshtewi was accused of theft and of having sex with another man, the New York Times reported.
In a briefing to the UN Security Council, Mr Mladenov stressed that international law limited the application of the death penalty to the "most serious crimes" and pursuant to a trial and appeals process that scrupulously follow fair trial standards.