Labour is considering disciplinary action against an AM who suggested Jewish people's security fears could be "in their own heads".
The Jewish Chronicle obtained a recording of Jenny Rathbone in which she also said hostile behaviour towards Jewish people was driven by the behaviour of the Israeli government.
Jewish leaders have described the remarks as "inexcusable."
Ms Rathbone has said she is "deeply sorry" for the remarks.
First Minister Carwyn Jones called the comments "totally unacceptable" and has submitted the matter to the general secretary of the Labour Party for investigation.
BBC Wales understands the recording was made at a question and answer event in her Cardiff Central constituency last year.
In it, she was asked for her thoughts about extra security measures at the Cyncoed Synagogue in Cardiff, and an increase in hate crime.
She responds by saying: "I think it's the failure to come to a peace settlement around Palestine and Israel.
"I think that the Israeli government's behaviour in occupying Palestinian lands [indistinct audio] and generally behaving like a conqueror is conducive to peace.
"And I think that's what drives people to be hostile to the Jewish community in this country.
"And I think the Jewish community has a responsibility to try and promote peace in the Middle East."
She added: "...the fact that the Jewish synagogue in Cyncoed is, is become one of these, you know, fortress is really uncomfortable.
"How much of it is for real and how much of it is in their own heads is really hard for an outsider to judge, but I think siege mentalities are also part of it."
On Wednesday Jenny Rathbone said: "I accept that comments I made last year were insensitive and have laid me open to accusations of intolerance.
"I've always appreciated the good relationship I've had with my local Jewish community and I apologise for any upset that my remarks may have caused to individual constituents and the wider Jewish community.
"I am meeting one of my local Rabbis later today to apologise directly.
"With levels of anti-Semitism on the rise in many western countries, and following the devastating attack on Pittsburgh synagogue, no one can or should downplay the fears and concerns that many Jewish people are experiencing.
"I had no intention of doing so and I am deeply sorry that I did.
"It is also not acceptable to suggest that the Jewish community are responsible for the actions of the Israeli Government."
Board of Deputies president Marie van der Zyl said the comments in the recording were "inexcusable".
She said: "The Labour Party should be ashamed that yet another example has emerged of its elected representatives blaming Jews for the tragedies that befall them. But we are long past being surprised."
And Stanley Soffa, chairman of South Wales Jewish Representatives said: "We certainly do not have a siege mentality.
"She has attended both the Cardiff Reform Synagogue and Cardiff United Synagogue, she has been made welcome when she has attended."
"I'm not surprised because some of the comments that she has made over the years have been perceived to be anti-Semitic," he added.
Condemning the the comments as "totally unacceptable", First Minister Carwyn Jones said: "I have been very strong in my condemnation of anything that either is or looks like anti-Semitism. The effect is the same either way.
"I can say I've had a complaint - or something I have treated as a complaint - which I have passed on to the general secretary of the Labour Party in London who is responsible for discipline at a party level.
"The chief whip, whose role this is, will be looking at what disciplinary action to take and will make a report to our group on Tuesday."
Welsh Labour leadership candidate Vaughan Gething said: "I do not agree with Jenny Rathbone's comments."
"We have to demonstrate leadership that is consistent with our values and stamp out anti-Semitism," he said.
His rival, Mark Drakeford, said: "Anti-Semitism is completely unacceptable and has no place at all in the Labour Party. Jenny Rathbone's comments were unacceptable. It's right that she has been referred to the Labour Party for investigation"
Welsh Conservative faith spokesman Mohammad Asghar said: "It seems that the disturbing tide of anti-Semitism has come to Wales and is no longer just Jeremy Corbyn's problem - but Carwyn Jones and his successor's too."