Mr Swinney also called for the state of Palestine to be recognised.
However, leaders of Scotland’s Jewish community have warned Mr Swinney’s “gesture politics” could see an increase in the “harassment and intimidation of Jews” in the country.
Almost 3,000 people have now signed an open letter to the First Minister calling for a retraction.
The letter from Scotland Against Antisemitism claims that Jews are leaving the country for Israel “out of fear” and has demanded a meeting with the Scottish Government to discuss protection for the Jewish community.
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There are around 5,000 Jewish people in Scotland, however the organisation said they the community has been victims in almost a fifth (17%) of all religiously motivated hate crimes in the last year.
Mr Swinney has been told that the Scottish Government has no foreign influence over Israel.
The letter also said that pulling a “tiny amount of funding” from a handful of companies “will not impact the Israeli government or change the course of the war”.
Leah Benoz, founder and director of Scotland Against Antisemitism, said: “The Scottish Government has no power over foreign policy, and the proposed funding cuts are tiny and will have no effect on events in the Middle East.
“Not one Palestinian life will be saved by these measures, but Jewish life in Scotland will be put further at risk.
“Our question to Mr Swinney is simple. Is our safety really a price worth paying for this kind of gesture politics?”
The letter to Mr Swinney also argued that an “exceptional standard of proof that can only be met in a court” is needed before genocide can be declared.
Leading experts from the International Association of Genocide Scholars (IAGS) has declared that Israel is committing genocide in Gaza.
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Mr Swinney echoed the genocide claim and urged Prime Minister Sir Keir Starmer to impose the “toughest and most severe sanctions” on Israel.
But the letter from Scotland Against Antisemitism said: “For the Scottish Government to endorse this modern-day blood libel will not save a single innocent life in Gaza, but it will embolden those who now use the language of genocide to justify the harassment and intimidation of Jews here in Scotland.”
“The human suffering in Gaza is real and cannot be understated, nor is it our intention to do so,” the letter added.
“But we must be absolutely clear with you about the real world impact of the measures your government has announced.”
A statement from Timothy Lovat, chair of the Jewish Council of Scotland, last week also described Mr Swinney’s actions as “disappointing”, warning it could “undermine the safety, security and wellbeing” of the Jewish community in Scotland.
A Scottish Government spokesperson said: “As the First Minister made clear in setting out his statement to Parliament, the Scottish Government deeply values our relationship with Scotland’s Jewish community and it is vital that they feel safe and supported.
“There can be no place for antisemitism or hatred of any kind in Scotland.”
The spokesperson continued: “The First Minister met with representatives of the Jewish community this week to assure them of this, and will continue to engage in dialogue with the community.
“The International Court of Justice has found a prima facie case that the Israeli government was committing genocide and the First Minister, along with many international leaders, shares the concerns that the actions of the Israeli government in Gaza constitute a genocide.”