Thugs who desecrated a Jewish cemetery may have been attempting to gain access to the graves, it has been claimed.
A gang of around eight youths were seen smashing headstones with hammers in Belfast.
During the attack, last Friday, they also smashed concrete slabs covering the graves, in an apparent effort to gain access to the tombs.
Jewish leaders said the cemetery was a "soft target" that had suffered decades of attacks, and claimed the desecration could have been linked to last month's anti-Israel protests at a football match in Scotland.
Police have rejected the claim.
Religious and political figures in Northern Ireland condemned the incident. Thirteen graves in the Jewish section of Belfast City Cemetery were vandalised.
Sinn Féin councillor Steven Corr said council staff had reported the damage was carried out by eight youths, supported by a larger crowd.
He described the attack as a "sad day" for Belfast and its Jewish community which, he said, "continues to make a most valuable contribution to the lifeblood of this city".
Belfast rabbi David Singer was in Israel celebrating his son's wedding when he heard the news.
He said: "It wasn't something that we would have expected. Up until now, Belfast, and in general Northern Ireland, has been good to the Jews. From what I've heard, it was a bunch of hooligans and they ran away like cowards into a large crowd when the police arrived. It's going to be very difficult to find them."
Michael Black, Belfast Jewish Community chair, describing the cemetery as a "soft target", added that there had been "a lot of very supportive reaction".
He said: "Obviously, people who have family buried there are very upset. We are very mindful of the rise of antisemitism throughout Europe.
"We have had very minor incidents here, but today a lot of the antisemitism tends to be linked to the issue of Palestine and the West Bank. Whenever that's in the news, the number of incidents rises.
"I have lived here all my life and never experienced any antisemitism. You get the odd jibe, but nothing major.
"You can name any previous incidents on one hand, which is why this has come as a hell of a shock."
Leslie Leopold, who oversees the management of the cemeteries for the synagogue said it was a "historic" graveyard and was not in current use.
The Jewish section of the council-run cemetery was established in 1863. Almost 300 Jews are buried there, with the last funeral held in 1964.
The community currently uses Carnmoney cemetery, north of Belfast, for burials.
Steven Jaffe, co-chair of Northern Ireland Friends of Israel, said: "There has been a long history of vandalism at the Jewish section since the 1970s. The tahara [purification] house was wrecked by vandals in 1972.
"In 2009, the section was in a terrible state as a result of anti-social behaviour. Many of the stones were missing or broken as a result of vandalism.
"The maintenance and repair of the section was turned around by the council, largely the work of a local Sinn Féin councillor, Tom Hartley."
Mr Black claimed the motive for the attack may lie beyond Northern Ireland.
He said: "The police have suggested that there may have been a link between this and what happened at the Celtic match last week."
Football governing body Uefa charged Glasgow's Celtic club after fans flew Palestinian flags at a match against Hapoel Be'er Sheva last month.
Scotland's two largest and most successful football clubs - Celtic and Rangers - have a cultural identity closely bound to Northern Irish politics. Celtic has a mainly Catholic following.
Both sides of the sectarian divide in Northern Ireland generally identify with the situation in the Middle East, with Catholic Republicans largely supporting the Palestinians, while Protestant Loyalists side with Israel.
The Belfast cemetery is based in a prominent Republican neighbourhood.
A Police Service of Northern Ireland (PSNI) spokesman said: "There is no evidence to suggest a link at this stage between the football match and the criminal damage caused to the graves."
No arrests had been made by Wednesday, but police said the investigation was ongoing.
Chief Inspector Norman Haslett said: "This is a particularly sickening incident, which we are treating as a hate crime.
"To disturb the sanctity of a cemetery in this way is completely unacceptable and I can assure the public that we will conduct a robust investigation in a bid to bring those responsible before the courts."
A BBC camera crew filming the desecrated graves on Tuesday experienced further antisemitism.
Evening news reporter Lisa McAlister's broadcast showed her explaining: "When we arrived this afternoon, there was a group of youths standing drinking, and as we walked through the gates to the Jewish section of the cemetery they began to shout antisemitic abuse."
Bishop Noel Treanor condemned the vandalism as "a blemish on our society".
He said it was "a tragedy that the long-present, beloved and treasured Jewish families of our community should suffer yet again such actions of disrespect, violence to the memory of their beloved dead and the regrettable outworking of a latent xenophobia".
Paul Maskey, Sinn Féin MP for west Belfast, said: "Visiting cemeteries can bring great comfort to grieving relatives and friends and it would be very distressing for anyone to have the grave of a loved one desecrated in this way.
"All graves and graveyards should be treated with respect."
There are thought to be around 300 Jews in Belfast, and the city's only synagogue has 80 members.
Former Belfast Lord Mayor Jim Rodgers called for an urgent review of security at the cemetery.
He said he would pursue the matter at the council's next meeting in a fortnight.