A school set up to promote peace and understanding between Arab and Jewish communities in Jerusalem has been hit by vandals who have daubed racist threats on its playground walls, including "Death to Arabs".

Teachers and pupils at the Max Rayne Hand in Hand Jerusalem School, the city's only Jewish-Arab school, also found sprayed on its walls, "Shoah [Holocaust] for the Arabs" and "Kahane was right" – a reference to the notorious rabbi whose ultra right wing political movement, Kach, was barred from contesting Israeli elections in 1988 and listed by the US State Department as a terrorist organisation in 2002.

Police are investigating two attacks at the school, which have raised concerns that right wing Jewish extremists now see co-existence projects as a target. The bilingual school has teachers as well as primary and secondary pupils from both communities. It is named after British-Jewish businessman, Max Rayne, who opened the school in 2007.

The attacks came just four days after similar threats were sprayed on the wall of a Greek Orthodox monastery in the city, and a car outside, including the words "price tag" – a term used by militant Jewish settlers to describe attacks on Palestinian property carried out in revenge for action taken by the Israeli military against illegal settlement outposts in the West Bank.

Three houses were demolished by the military last year in the Jewish West Bank outpost of Migron, which is illegal in Israel as well as international law. Since then there has been a spate of attacks on Palestinian property in the West Bank including mosques.

The Abraham Fund, which sponsors co-existence projects, has raised concerns "price tag" attacks are now being aimed at education for shared living between Arabs and Jews in Israel. A spokesman said: "These attacks are on a place [the school] that represents the wish of Arabs and Jews to build together a better future for their children."

Paz Cohen, the Jewish joint chairman of the Max Rayne Hand in Hand school's parents' committee, vowed the school would continue its work: "It has been a huge success and these radicals don't know how to handle this reality. It is very hurtful to see this graffiti, it is not just against Muslims but against Jews, against everyone. It puts a strain on democracy but it will make our group bigger and stronger."

Mr Cohen said his father had left Nazi Germany to escape a regime which had also started with a small group of radical racists, adding of the present day Jewish extremists: "They have to be aware of the acts we have historically suffered ourselves." He added he had been heartened by the swift response of the police and Ministry of Education, and by a letter from the Speaker of the Knesset, Reuven Rivlin, which had been read out to pupils after the attacks, who called on the authorities to bring the perpetrators to justice.

One parent of a pupil said later: "Some of the younger Arab kids are scared, while some of the older ones don't understand why people would do this. And there is some anger."