Palestinian sources said they expected that Abbas would hold a long-awaited meeting with Ehud Olmert, the Israeli prime minister, in the nexst few days. Israeli officials were not immediately available to comment.
While such a meeting would be seen as a possible spur to reviving peace talks between Israel and Abbas, Olmert has said the Palestinians could expect little until a soldier held captive in Gaza since June was freed.
Olmert refuses to deal with Hamas, which refuses to recognise Israel.
Fatah accused Hamas of violating the latest truce in the wake of the deaths of its two gunmen around dawn on Wednesday.
"Unless Hamas stops its violations, the second agreement ... could be in danger," Tawfiq Abu Khoussa, a Fatah spokesman, said.
Hamas said its forces were returning fire in the incident, and said it was committed to the second ceasefire.
A previous truce broke down within hours.
A senior aide to Abbas said the president planned to issue a decree next week to lay the legal foundations for parliamentary and presidential elections, which Hamas - elected to power in January - has described as a "coup" and unconstitutional.
Hamas has said it would boycott any polls. No date has been announced.
Hamas and Fatah tried for months to form a unity government to end a power struggle, but talks foundered.