A petition demanding an end to "gender discrimination against women" by El Al Airlines, the flag carrier of Israel, has been launched after flights were delayed when some ultra-Orthodox men refused to sit next to women.

In the petition, posted at change.org, Sharon Shapiro, from Chicago, says: "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 do not trump another person's civil rights."

The petition, which at the time of writing has more than 3,000 signatures, was launched as a response to women being asked to change places by ultra-Orthodox Jewish men on an El Al flight, so the men did not have to sit next to them.

Under the section of Halakha, or Jewish law known as "negia", meaning "touch" in Hebrew, some ultra-Orthodox Jewish believers insist they must sit separately from members of the opposite sex in activities such as travelling.

The law, derived from passages in Leviticus 18 which forbid men approaching any close female relative or menstruating woman "to uncover her nakedness", applies to cars and trains as well as planes.

The US Jewish magazine, Tablet, reports: "Last week we published Elena Sztokman's account of traveling from the United States to Israel when an Orthodox man seated next to her on the airplane refused to sit next to her because she was a woman. The flight was delayed 20 minutes until a new seat was found for the passenger.

"That same week, an El Al flight from New York was delayed significantly when a group of Orthodox men refused to take their assigned seats next to women, reportedly offering passengers money to switch seats."

The petition states that if a passenger was being verbally or physically abusive to airline staff, they would immediately be removed from the plane. If a passenger was flouting the rules for take-off, thereby causing flight delay, they would immediately be removed from the plane."

It continues: "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?"

It suggests: "If El Al Airlines wants to truly accommodate all of its passengers, it will reserve a few rows of separate sex seating on every flight, where for a fee, those passengers who need such seating can pre-book their seats and not annoy or coerce other passengers before take-off to change seats with them - thereby avoiding arguments, bullying, and delayed take-off.

"If, under government regulations forbidding airline carriers to offer segregated seating based upon sex, El Al is unable to carry out such religious accommodations directly, perhaps indirectly El Al can refer such requests to independent private travel agencies who buy block seating for such purposes. Religious passengers could then purchase tickets through those private agencies that will guarantee same sex seating."

The Washington Post reports that women's rights advocates have recorded similar incidents over many years such as in offices, on public buses and even streets in some areas of Israel.

In one statement in relation to one of the flight delays, the airline said: "If it is found that there are possibilities for improvement in the future, those suggestions will be taken into consideration." In a subsequent statement, El Al added that that the airline makes "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."

The controversy is mirrored by one in London, when the local authority in Stamford Hill, an area where many ultra-Orthodox families live, took down posters that instructed women to walk down a particular side of the road because they were deem end "unacceptable".

Hackney Council took down the posters after an ultra-Orthodox or Haredi group put them up for a religious procession, to make sure there was no accidental touching between men and women. The posters were intended only for members of that community and to apply to that particular event, a spokesman said.