"We oppose, on principle, aggression against anyone, and the spilling of blood," he told a group of Israeli MKs visiting his headquarters in Ramallah.
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The girl, Noam Glick, was lightly injured Saturday night while she was playing in the yard of her home in Psagot, a Jewish settlement located north of Ramallah in the West Bank. No one else was hurt in the incident.
Paramedics who were alerted to the scene evacuated the girl, who was fully conscious, to Jerusalem's Shaare Zedek Medical Center. She suffered injuries to her upper torso, and the doctor who was treating her said it was unclear whether she had been shot or stabbed.
Police said it was probably a "terror" attack.
Medics at the Jerusalem hospital said on Monday that her condition was improving.
Abbas spoke as Israeli forces closed in on an area in the West Bank town of Al-Bira, near Ramallah, in an arrest operation linked to the Psagot attack, an AFP correspondent said.
Palestinian media reported that IDF troops raided the town of Al-Bira, near Ramallah, Monday afternoon. The forces arrested two brothers who live in the town after searching their homes. It remains unknown whether there is any connection between this arrest and the Psagot attack on Saturday.
Abbas objected to the unilateral Israeli operation, insisting the Palestinian Authority should take responsibility for finding the culprits.
"The Israeli army's incursions are unjustified. There's security coordination with us, so why carry out these raids that harm (our efforts)?" Abbas said.
"Seven years ago we (the Palestinian Authority) began security cooperation (with Israel)," he said, describing coordination on security as functioning at "100 percent."
Prime Minister Benjamin Netanyahu had condemned the "hateful attack" in Psagot and said he held the Palestinian leadership responsible even though the attack took place in an area of the West Bank under full Israeli control.
"As long as the incitement continues in the Palestinian official media, the Palestinian Authority cannot absolve itself of responsibility for events of this sort," he said at the start of the weekly cabinet meeting on Sunday.
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