Israeli right wing activists made a mock body covered in fake blood during a protest at the site of the terror attack. Reuters

The Israel Defense Forces (IDF) have arrested the father and the brother of a key suspect in the hit-and-run attack in the occupied West Bank which left three soldiers injured, according to local media reports.

Israeli forces entered the village of Beit Awa, near the flashpoint city of Hebron, and informed the Mesalmeh family that their son Hamam was being searched for in relation to the attack, Israeli Radio reported.

"The IDF is conducting a widespread search in the region to locate the vehicle and its driver," the army said in a statement.

According to Palestinian news agency Safa, other members of the Mesalmeh family may have been detained in the raid while suspected accomplices to the attack were arrested in the al-Aroub refugee camp near Jerusalem.

The attack saw a van plow into three soldiers who were standing on the side of the road near the al-Aroub refugee camp before driving off. The white van was later abandoned and found by Israeli troops. The driver remains at large.

Following the attack, Palestinians threw rocks at Israeli cars as they drove past the location of the accident, The Times of Israel reported.

The attack came on the same day that an Arab-Israeli drove his car into two crowds of civilians in Jerusalem, killing one and injuring 13. Islamist militant group Hamas claimed responsibility for the hit and run attack and also called for a third intifada - or uprising - in the city to defend the Al-Aqsa Mosque, the third-holiest site in Islam.

The attack saw Ibrahim al-Akri, from the Palestinian Arab neighbourhood of Shuafat in East Jerusalem, shot dead by Israeli security forces after he had driven his car into the crowds.

Hamas spokesman Mushir al-Masri praised al-Akri for his "heroic operation" and called him a "martyr".

"We congratulate the activity carried out by Jerusalem's blessed heroes that targeted soldiers and security men," the terror group said in a statement.

"This was a result of the crimes of the Zionists who continue to attack the worshipers and to violate the Palestinians' holy sites," they added.

"We call on the people of Jerusalem and the West Bank and all of the Palestinians to carry out more of these activities with full force in order to defend al-Aqsa."