Israel’s national airline, El Al, has been criticised for allowing ultra-orthodox Jewish men to disrupt flights by refusing to be seated next to women.

A petition on change.org is demanding that the carrier “stop the bullying, intimidation and discrimination against women on your flights”.

One flight last week, from New York’s JFK airport to Tel Aviv’s Ben Gurion airport, descended into chaos according to passengers, after a large group of haredim, or ultra-orthodox Jews, refused to take their seats next to women, in accordance with strict religious customs.

The episode has prompted other women to come forward with similar stories on international flights to and from Tel Aviv.

Amit Ben-Natan, a passenger on last week’s El Al flight from New York, said take-off was delayed after numerous and repeated requests by ultra-orthodox men for female passengers to be moved.

“People stood in the aisles and refused to go forward,” she told the Ynet website. “Although everyone had tickets with seat numbers that they purchased in advance, they asked us to trade seats with them, and even offered to pay money, since they cannot sit next to a woman. It was obvious that the plane won’t take off as long as they keep standing in the aisles.”

Another passenger on the flight, named only as Galit, said ultra-orthodox passengers had suggested she and her husband sit separately to accommodate their religious requirements. She refused, but added: “I ended up sitting next to a haredi man who jumped out of his seat the moment we had finished taking off and proceeded to stand in the aisle.”

On a different flight, Elana Sztokman, a former executive director of the Jewish Orthodox Feminist Alliance, refused to accede to a request to move seats, triggering “frantic negotiations”, she said, between ultra-orthodox men and airline staff.

“What happened to me on this flight isn’t that different from what happens on almost every flight,” she told Voice of Israel radio. “You get on a plane, and the plane is about to take off but a whole bunch of ultra-orthodox men start playing around, moving around, whispering, moving back and forth trying to find different seats … Anyone who’s ever travelled on El Al has experienced this.”

Sharon Shapiro, from Chicago, the organiser of the online petition – which had attracted about 1,000 backers by Tuesday morning – said it was “not right that female passengers are being intimidated or harassed. It’s one thing to ask nicely, but if someone says no, they should not be put under pressure.”

There was a genuine dilemma for some ultra-orthodox Jews. “What most people don’t understand is that it’s not personal”, but considered by some to be a religious obligation.

Airlines should seek a way of accommodating the religious requirements of passengers without breaching others’ civil rights, she said. “I’m not quite sure why El Al asks passengers to sort these things out among themselves. It would be better if people can get on a plane knowing they’re sitting somewhere they feel comfortable. Otherwise, it adds to tensions and misunderstandings between religious and secular [passengers].”

The petition says: “If a passenger was being verbally or physically abusive to airline staff, they would immediately be removed from the plane … If a passenger was openly engaging in racial or religious discrimination against another passenger or flight attendant, they would immediately be removed from the plane. Why then, does El Al Airlines allow gender discrimination against women?

“Why does El Al Airlines permit female passengers to be bullied, harassed, and intimidated into switching seats which they rightfully paid for and were assigned to by El Al Airlines?

“One person’s religious rights does not trump another person’s civil rights.”

It suggests that El Al reserves a few rows of segregated seating available in advance for a fee.

Among comments posted on change.org, Judith Margolis from Jerusalem said: “The behaviour involving harassing women in the name of religious observance is outrageous. That airlines allow some passengers to disrupt flights is unacceptable.”

Myla Kaplan of Haifa said: “I no longer feel comfortable flying on El Al due to the bullying and delays and general humiliation of being asked to move out of a seat I reserved in advance.”

In a statement, El Al said it made “every effort possible to ensure a passenger’s flight is as enjoyable as possible while doing our utmost to maintain schedules and arrive safely at the destination.

“El Al is committed to responding to every complaint received and if it is found that there are possibilities for improvement in the future, those suggestions will be taken into consideration.”

Female passengers on other airlines flying to and from Israel, such as British Airways and easyJet, have also been asked to move seats at the request of ultra-orthodox men. Some airlines close toilets for periods during flights to allow men to gather to pray.

The outcry over flights comes against a backdrop of moves by hardline ultra-orthodox communities in Israel to impose dress codes on women, restrictions on where they can sit on public buses, segregated checkout queues in supermarkets and the removal of women’s images from advertising hoardings.

Sztokman – whose flight came at the end of a US speaking tour on her new book, The War on Women in Israel: A Story of Religious Radicalisation and Women Fighting for Freedom – said such demands had increased over the past decade.

“A lot of what we’re seeing today … is about the erasure of women’s faces from the public sphere, the erasure of women’s names from newspaper articles, the refusal to let women talk on radio stations

“It’s a whole array of practices of women’s exclusion and women’s degradation that has got much worse.”

• This article was amended on 3 October 2014 to clarify Elana Sztokman’s job title.

