The threat comes from the far-left and right, from Islamic extremists and from the "middle of society" - studies over the decades show a steady 20 per cent of the population of "Western" countries hold antisemitic views.
The demonisation of Israel, a key tool of the worldwide BDS campaign, is on the rise, and recent attacks by Islamic extremists targeting Jews and Jewish institutions have put communities around the world on red alert.
Fear itself can undermine the stability of communities, Mr Forman said.
"If things get worse, some of the smaller, weaker communities on the continent could fall apart," added Mr Forman, in Berlin to attend the Inter-Parliamentary Coalition for Combating Antisemitism, which brought together 140 legislators from nearly 40 countries.
"People make aliyah, they go to other countries in Europe, to the US, or they assimilate. Why be Jewish if your kids and you are threatened?
"You don't need everyone to leave for a community to fall apart. If communal leadership goes, you essentially disintegrate."
In fact, one third of victims of antisemitic attacks in Europe were considering emigrating, according to the 2013 survey on discrimination and hate crime against Jews in EU member states, conducted by the EU Agency for Fundamental Rights. Jews in France (50 per cent) and Hungary (47 per cent) were the most likely to have thought along those lines.
But "even [Jewish] communities that have not experienced particular forms of violence are worried, if they read about violence in France, in Belgium, in Copenhagen," Mr Forman said. "I can't think of a community I haven't heard that from."
Guards and surveillance cameras are not the only answer, and security is a "Band-Aid," he said. Education and civic engagement are also essential. "How do we interact with the social media, and internet? How do we push back against hate speech in those venues? We don't have answers yet."
At times, Mr Forman finds himself intervening in concrete ways: prodding governments to take the concerns of Jewish communities seriously.
"Many national governments - Germany, France, the UK - are fantastic. But other places [are not so good]… the US embassy is one place where Jewish communities under great pressure know that they have a friend."
When Jewish communities in continental Europe expressed fear of violent anti-Israel demonstrations during the Gaza crisis of the summer of 2014, Mr Forman stepped in.
In a city he would not name, "law enforcement authorities lost control of the street on the first weekend". Mr Forman spoke to the US Embassy Deputy Chief of Mission, and "within 24 hours I heard from that Jewish communal leader: 'I don't know what you folks did, but suddenly the security people were out in force'."
Rabbi Andrew Baker, director of International Jewish Affairs for the American Jewish Committee, said: "If he goes in somewhere where there is an issue to be addressed, governments take the issue more seriously."
Mr Forman said it was a combined effort. "We need our democratic allies in Europe to help us and help Jewish communities," he said, "and we need civil society to step up."
Mr Forman was born in the Washington, DC area in 1952 and grew up near Cleveland, Ohio. After earning degrees from Harvard University and Stanford University, he returned to the US capital, where he lives today with his wife, Caryn Pass. They have three children.
He worked for 30 years for Jewish communal bodies, including stints with Aipac, the National Jewish Democratic Council and as Jewish Outreach Director for US President Barack Obama's campaign.
His parents - born in the USA to Jews of Eastern European background - taught him to appreciate Jewish values and gave him a thirst for knowledge of Jewish history, which one cannot study "without understanding and learning a lot about antisemitism and how Jewish communities have both flourished… and also suffered".
But there are many good stories to be told, he said. "There are amazing things going on," including projects run by Jews, Muslims and Christians dedicated to fighting antisemitism and other forms of discrimination. "These people every day are in the trenches; they do amazing work."
