Ahmad al-Batsh, a pro-reform Palestinian legislator, said unknown assailants fired a volley of shots at his house and at his parked car in the early hours on Wednesday in the West Bank village of Bir Nabala, near Jerusalem.
The shooting caused damage but no one was hurt.
Al-Batsh called for Prime Minister Ahmad Qurayaa and his interior minister to resign over their failure to curb lawlessness.
"I hold the Palestinian prime minister, security and interior ministers fully responsible for the security disorder in this country," he told Aljazeera.
Al-Batsh said: "I join my voice to those of all Palestinians calling on this authority, particularly the security minister, to either take care of such cases or resign."
The PA is struggling to end the
reign of armed political factions
He has refused to accuse any side and urged the Palestinian Authority to open an immediate investigation.
"The Palestinian security chief should investigate this case, find the suspects and maintain security and safety of the Palestinians," al-Batsh said.
The incident was the latest in a series of attacks on Palestinian politicians seeking reforms after decades under the corruption- and chaos-ridden rule of Yasir Arafat, whose loyalists still largely dominate the security services.