The latest spiral of violence intensified when a blast on Friday killed 16 people at a Hamas rally in Gaza. One of the victims, a 12-year-old boy, died of his wounds on Sunday.
Hamas blamed Israel and militants fired at least 40 rockets into the Jewish state in response, though Israel denied responsibility and the Palestinian Authority said it appeared to be an accident caused by Hamas members carrying explosives.
Hamas vowed revenge for the latest Israeli strikes and raids. Spokesman Mushir al-Masri said the violence could "open the doors to hell." Hamas leaders would take extra precautions against Israeli attacks, he said.
Hamas has so far largely abided by a truce that Abbas agreed with Israel in February and which helped smooth the Israeli pullout from Gaza.
As well as condemning the Israel strikes, Abbas has also strongly criticized militants for keeping explosives in built-up areas, calling their actions a "massacre".
U.N. Secretary-General Kofi Annan and the European Union said they were concerned by the escalation and urged restraint.