Another MSP said the attack has meant that Jewish communities in Scotland "do not feel safe".
Their comments come as two people have been killed after a car was driven at members of the public and a man was stabbed outside a synagogue in Manchester this morning.
Four others are said to be in hospital.
The attacker is understood to have died after being shot by police.
Greater Manchester Police Chief Constable Sir Stephen Watson said two members of Manchester's Jewish community have died as a result of the attack.
Police say a "large number of people" were worshipping at the synagogue on Yom Kippur - the Jewish faith’s holiest day during which people reflect on the past year and atone for their sins.
Speaking on the attacker, Constable Sir Stephen Watson said he was wearing a vest "which had the appearance of an explosive device".
At First Minister's Questions today, Mr Swinney said: "Can I express my horror at the attack on the synagogue in Manchester this morning.
"This attack came on Yom Kippur, the holiest time of the Jewish calendar. My thoughts are with the victims, their families and all of the Jewish Communities in Scotland and across the United Kingdom and our record our thoughts and appreciation to the emergency services and the first responders for the speech of their response.
"Anti-Semitism is an evil we must confront and stand resolutely against and I know that the whole chamber speaks with one voice on this important issue."
Jackson Carlaw, MSP for East Renfrewshire, said the attack has left Jewish communities feeling unsafe.
Mr Carlaw wrote on X: "This horrendous attack in Manchester on the holiest of all days, Yom Kippur, shocks and appals us all. Emotions are understandably acute. Jewish communities do not feel safe. Anti Semitism is abroad in the UK & far too many have been complacent. It must be confronted & defeated."
The First Minister has said Police Scotland will now be considering security measures to take following the incident which he said will have his "full support".
Speaking to journalists after First Minister's Questions, Mr Swinney said: "On security and safety for places of worship, and especially synagogues and Jewish places of worship, these are issues which obviously cause me significant concern. Individuals must be able to live in safety in our country and they must be able to worship in safety.
"Police Scotland will be considering what steps need to be taken to make sure communities can be assured of their safety and they of course have my full support and encouragement to do so."
Police Scotland has confirmed they are carrying out additional patrols around synagogues and other Jewish venues.
Assistant Chief Constable Stuart Houston, lead for Organised Crime and Counter Terrorism in Scotland, said: “Our thoughts are with the Jewish community, the victims, families, and everyone affected by the incident in Manchester.
“Police Scotland officers are already carrying out additional and dedicated patrols around synagogues and other Jewish venues as part of our existing policing plan for the Jewish High Holy Days.
“Following the incident, we are actively communicating with faith leaders and community leaders.
“While there is no intelligence to suggest any specific threat in Scotland, I want to take this opportunity to ask the public to remain alert but not alarmed. You should remain vigilant and report any suspicious activity to Police Scotland.
“Policing in Scotland has strong relationships with the public and we are grateful for the ongoing support of all our communities.”
Other politicians across the Holyrood chamber noted their concerns following the attack during First Minister's Questions.
Scottish Conservative leader Russell Findlay began by paying his respects to the Jewish community following the attack in Manchester this morning as he described the incident as "horrific".
Scottish Labour's Anas Sarwar echoed Mr Swinney's and Mr Findlay's remarks as he said he was "horrified" by the news as he expressed his thoughts are with all those affected and the wider Jewish community.
He added: "Yom Kippur should be a time of peace and reflection but instead they have been the victim of hate and violence."
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The Prime Minister has ended a trip to Denmark early and will chair an emergency Cobra meeting in London this afternoon.
Police said it had “declared Plato” – the national code-word used by police and emergency services when responding to a “marauding terror attack”.
The Prime Minister said he was “appalled” at the attack, adding: “The fact that this has taken place on Yom Kippur, the holiest day in the Jewish calendar, makes it all the more horrific.”
In a statement, the force said: “Police were called to the Heaton Park Hebrew Congregation Synagogue, on Middleton Road, Crumpsall, at 9.31am by a member of the public, stating he had witnessed a car being driven towards members of the public and one man had been stabbed.”
The force said it declared a major incident at 9.37am.
[SRC] https://www.heraldscotland.com/news/25512052.john-swinney-condemns-manchester-synagogue-attack-horrific/
