Israel carried out a missile air strike on a van in Gaza carrying resistance fighters and rockets. The attack killed 11 Palestinians, nine of them civilians, and wounded about 30 in the deadliest such attack in nearly four years.
Abbas said: "What Israel is doing is called state terrorism. This state terrorism will not shake us."
The Hamas-controlled cabinet condemned the "ugly massacres" and the armed wing of the ruling Islamists separately threatened to avenge the deaths with further rocket attacks on Israeli territory.
Dr Jumaa al-Saqqa, a spokesman for al-Shifa hospital, told Aljazeera that a number of Palestinians were also wounded in the strike in Salah al-Din Street, the main road through the coastal strip.
Hospital officials and witnesses are reported as saying that two schoolchildren are among the dead.
According to Aljazeera's correspondent, the first strike hit a car carrying members of al-Quds Brigades, the military wing of Islamic Jihad.
Palestinian witnesses said several missiles were fired, and one of them hit the car.
The second missile came two minutes later, after a crowd had begun to gather around the scene of the attack, witnesses said.
The correspondent said two ambulance drivers were among the dead.
The number of dead is expected to rise, as hospital sources say some of the wounded are in critical condition.