Members of the Catholic movement urged ministers to "condemn publicly" the deaths of Palestinians, which come amid a series of protests in recent weeks.
Writing in the Guardian on Thursday, they said: "Each week, Israel has placed troops on the security border with Gaza with the intention to shoot to kill Palestinians demonstrating.
"So far, 35 Palestinians have been killed and more than 1,500 injured with live ammunition.
"Instructions to shoot to kill were given in advance."
Thousands of Palestinians have protested along Gaza's sealed border with Israel in demonstrations said to be highlighting the forced expulsion and fleeing of Palestinians from their land when the state of Israel was created in 1948.
Israel has previously defended the actions of its military, saying soldiers were responding to those "actively attacking the fence".
The letter was also signed by MPs and peers, including Labour's Grahame Morris and Tommy Sheppard from the Scottish Nationalist Party.
It continues: "It is right for the British government to comment on hostile actions by foreign states in breach of international law wherever they occur - on UK territory, in Syria or in Yemen.
"But the silence of the prime minister and the foreign secretary on Israel's premeditated killings is deafening."
Signatories also include the Palestine Solidarity Campaign, the National Union of Teachers, the GMB union, the Aslef train drivers union and Baroness Tonge.
They called upon the Goverment to support a United Nations investigations into the killings and "to ensure UK arms, finance and trade are not used to support Israel's unlawful actions".
Premier has approached the Foreign Office for a response.
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