The Gaza-based Palestinian Centre for Human Rights called for "an immediate moratorium on the use of the death penalty as a form of punishment because it violates international human rights standards."
Authorities in Hamas-controlled Gaza sentenced a 24-year-old to death by hanging on charges of murder, and a court in Hebron in the West Bank handed a sentence to another man on charges of collaboration with Israel, it said.
Under Palestinian law, collaboration with Israel, murder and drug trafficking are all punishable by death.
All execution orders must be approved by the Palestinian president before they can be carried out, but Hamas no longer recognises the legitimacy of Abbas, whose four-year term ended in 2009.
Hamas executed 18 men in August for alleged collaboration with Israel during the 50-day Gaza war, having executed two others in May on the same charge.
The PCHR's statement today was directed specifically at the PA, which it said had issued 157 death sentences since its creation in 1994, and so far carried out 32 of them.