West Yorkshire police said the 59-year-old spoke to detectives voluntarily after complaints about a speech he gave in Leeds this month in which he said: "We don't want any Israeli goods, we don't want any Israeli services, we don't want any Israeli academics coming to the university or the college, we don't even want any Israeli tourists to come to Bradford, even if any of them had thought of doing so."
A police spokesman said that the matter would be referred to the Crown Prosecution Service for their consideration once inquiries are completed.
Galloway said: "This is a monumental – and monumentally expensive – waste of police time set off by people who apparently find it excusable to incinerate innocent children and babies. I will not suffer any attempts to have my freedom of speech curtailed and I am confident that at the end of this charade my right to speak the truth will be upheld."
The news came as a prominent Muslim community leader in Bradford accused Galloway, who is the MP for Bradford West, and the Israeli embassy of creating disharmony in the city.
The row escalated on Tuesday after Daniel Taub, Israel's ambassador to the UK, visited Bradford and held meetings with Jewish groups and prominent councillors. According to the embassy, he came at the invitation of members of the city's small Jewish community and supporters of Israel, after Galloway said Israeli tourists were unwelcome in the city.
During his visit on Monday, Taub said: "In the best spirit of Yorkshire, the real voice of Bradford knows that there has only ever been one good boycott – and that's Geoff Boycott."
He also tweeted a picture of himself holding an Israeli passport outside city hall and another with an Israeli flag in the Greengates area of the city: an act described as a "deliberate provocation" by Zulfi Karim, secretary of the Bradford Council for Mosques.
Karim said on Tuesday: "For an ambassador to unfurl an Israeli flag by a Welcome to Bradford sign is a deliberate provocation and not the behaviour I would expect of an ambassador of one of the world's most important countries."
He called on Galloway and Taub to stop using the city for their own political ends, saying: "This is to Mr Galloway and the ambassador: please do not bring your politics on to the streets of Bradford to create disharmony among our communities. If you have concerns, share them in your embassy or in parliament or in a neutral place, not in Bradford."He added: "We work in harmony in Bradford and we support our Jewish community. Last year it was the Muslim community which helped to secure the sustainability of the city's last synagogue."
With only 299 Jews left in the city, the final synagogue was under threat of closure when members could not afford to repair the roof, until local Muslims kickstarted a campaign to save the 133-year-old building.
In his speech on Monday, Taub praised the cross-cultural understanding in Bradford. "This real Bradford has a great deal to teach the world about a multicultural city where Christians, Muslims, and Jews live, work, and cooperate together. Here, the historic synagogue thrives thanks to the support of the Muslim community. It's a much-needed model of how people who may not agree about everything can still listen to each other, hear each other, and treat each other with genuine respect."
On Twitter on Tuesday, Galloway called on Bradford council to table a motion of no confidence in the leader, Labour's Dave Green, who met with Taub in city hall on Monday along with his Conservative and Liberal Democrat counterparts.
Green said he met Taub "just as I would meet the ambassador of any other country" after the embassy asked for a meeting with prominent local councillors. He said he welcomed the opportunity to raise with Taub "concerns that exist within the Bradford community about the conflict in Gaza".
Green said he also wanted to refute Galloway's claims, which "give an unjust and unfair view of the city".
"By making these ludicrous and outrageous statements, Galloway is doing something very dangerous because what it does is cause tension within communities in Bradford," he said.
Jews in the city had raised concerns about an increase in verbal abuse of late, said Green. "You may like to ask Galloway how he is going to identify Israeli citizens. It's one of those statements, which may get him a round of applause among his acolytes but which is underpinned by something really dangerous."
He accused Galloway of playing politics and using the conflict in Gaza to raise his own political profile locally and internationally. On Twitter on Monday night, Galloway wrote: "I think Labour's open invitation that 'Israelis are welcome in Bradford' and the ambassador's furtive visit ensured my re-election, no?"
Galloway won a landslide victory in a byelection in the Bradford West constituency in 2012, which he dubbed the Bradford Spring.
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