Palestinian students demonstrate in Gaza City on Wednesday to denounce recent clashes between Palestinians and Israeli security forces in the occupied West Bank and Jerusalem's flash point Al-Aqsa mosque compound. Photo: AFP

New violence rocked Israel and the West Bank on Wednesday, including a stabbing in annexed east Jerusalem, even as Israel and Palestinian president Mahmud Abbas took steps to ease tensions.

The knife attack in Jerusalem's Old City, in which a Palestinian woman stabbed a Jewish man before being shot and seriously wounded, was the second in the walled heart of the city in days.

An Arab man also allegedly stabbed a soldier in central Israel and stole his weapon before being shot dead by police, while in the West Bank settlers shot and seriously wounded a Palestinian after a stone throwing incident.

Israeli Prime Minister Benjamin Netanyahu postponed a visit to Germany set for Thursday to tackle the violence that has raged for three weeks despite appeals for calm.

Israel lifted age restrictions from Wednesday on Muslims praying at the sensitive Al-Aqsa mosque compound, swiftly welcomed by Washington, to ease tensions.

In Wednesday's Old City attack not far from the mosque compound, police said that an 18-year-old Palestinian woman stabbed a 35-year-old Jewish man in the back and lightly wounded him. The man, who was armed, managed to draw his gun and shoot and seriously wound his attacker, police said.

Separately, in Kiryat Gat in central Israel, police shot dead an Arab man after he allegedly wounded a soldier with a knife and took his weapon, authorities said. An incident in the occupied West Bank saw Jewish settlers shoot and seriously wound an 18-year-old Palestinian near Bethlehem, the Red Crescent and witnesses said.

In the same area, where both Israeli settlements and Palestinian villages are located, a group of Palestinians had sought to take an Israeli woman from her car and possibly kidnap her, said Israeli military spokesman Arye Shalicar.

According to Shalicar, settlers fired in the air and she was able to escape.