Hundreds of olive trees have been uprooted, burned or cut down by extremist settlers since the annual harvest got under way in the West Bank this month, prompting calls for the Israeli authorities to protect Palestinian farmers and their property.

According to the United Nations, more than 870 trees were vandalised in the first week of the harvest, which began in most places on or after 5 October. A coalition of four Israeli human rights organisations said more than 450 trees had been damaged over the past week.

The damage is usually discovered when Palestinian families arrive at their groves to gather the fruit. Sometimes Palestinians are attacked during the harvest itself.

Settler attacks on olive groves have increased over recent years. Since the beginning of this year, a total of 7,180 Palestinian-owned trees have been vandalised by settlers, according to the UN's office for the co-ordination of humanitarian affairs. Last year about 10,000 trees were uprooted or vandalised.

Robert Serry, the UN's special co-ordinator for the Middle East peace process, said the damage and destruction of trees was reprehensible. "Israel must live up to its commitments under international law to protect Palestinians and their property in the occupied territory so that the olive harvest – a crucial component of Palestinian livelihoods and the Palestinian economy – can proceed unhindered," he said.

Hanan Ashrawi, a member of the Palestine Liberation Organisation's executive committee, said settlers were launching attacks under the protection of the Israeli military.

In a letter to diplomats, she appealed to international missions to send observers to at-risk olive-picking areas to monitor abuses by settlers and soldiers.

"In the past month alone, Israeli settlers uprooted 300 trees in al-Mughir and Turmusaya villages, cut down 120 trees in Nablus, destroyed 100 olive saplings and 60 vine trees in al-Khader village, uprooted 40 trees in Ras Karkar, and assaulted and hospitalised three Palestinian farmer and injured one other," she wrote. According to Oxfam, there are about 9.5m olive trees in the West Bank.