Some Gaza residents ventured on to the streets for the first time in days to find masked fighters manning checkpoints and most stores closed despite the latest ceasefire deal.
More than 80 Palestinians have been killed in the fighting since December, when unity government talks between Hamas and Fatah broke down and Abbas called for new elections.
Fawzi Barhoum, a Hamas spokesman, said its fighters were abiding by the truce. He accused Fatah of failing to withdraw its forces from the streets.
Tawfiq Abu Khoussa, a Fatah spokesman, accused Hamas of planting bombs on key roads and shooting from rooftops into a main security compound.
Fatah and Hamas officials said further talks would be held on Sunday on implementing the terms of the truce.
In a related development, Shimon Peres, the Israeli deputy prime minister, has said Israel does not intend to intervene in the Gaza Strip, adding that any attempt of this kind would put Israel in a difficult situation.