Nickolay Mladenov told the Security Council that public executions are prohibited under international human rights law and that any such killings in the Gaza Strip would be carried out without the approval of Palestinian President Mahmud Abbas, which is required under Palestinian law.
"I urge Hamas not to carry out these executions and call on President Abbas to establish a moratorium on the implementation of the death penalty," Mladenov told the council by video-conference.
The death penalty can be applied only to the most serious crimes following a judicial process that upholds fair trial standards, the envoy said.
"I have serious doubts as to whether capital trials in Gaza meet these standards," he added.
Thirteen men, most convicted of murder connected to robberies, are currently awaiting execution, according to Hamas officials.
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Hamas, which runs the Gaza Strip, does not recognize Abbas's legitimacy.
The authorities announced on Sunday that they are planning to carry out a series of public executions.
The last public executions in Gaza took place during the most recent war with Israel in 2014, when a firing squad from Hamas's armed wing killed six men.
Nine death sentences were handed down in the Gaza Strip in 2015 and two in the occupied West Bank, run by the Palestinian Authority, according to the Palestinian Centre for Human Rights.
Around 10 more have been handed down in Gaza so far this year.
Mladenov also warned that a recent upsurge in violence between Israel and Hamas could lead to another war.
A ceasefire agreed in August 2014 "needs to be vigorously upheld by all sides if we are to avoid slipping into another devastating conflict," he said.