She then took them on a tour of Tel Aviv, visiting the city's university, a museum, a shopping mall and the beach, which she noted none of them had ever seen even though it is only about 40km from their village.
Gisha, an Israeli human rights group, said Israel introduced a permit system to limit Palestinian movement out of the West Bank in the early 1990s about the time the young women were born.
Ms Hammerman wrote that the only dangerous moment during the trip was when a plain-clothes policeman stopped them and asked for the women's identity cards. Ms Hammerman lied to the officer, telling him that the women were Palestinians from East Jerusalem and therefore entitled to enter Israel.
In June, Yehuda Weinstein, the attorney general, was reported to have approved a police investigation of Ms Hammerman after a settler organisation, the Legal Forum for the Land of Israel, complained.
The ranks of Ms Hammerman's supporters have swollen since the group placed an advertisement, titled "We refuse to obey", in Haaretz this month. The ad said the group was "acting in the spirit of Martin Luther King", the US civil rights leader, and demanded that Palestinians be treated as "human beings, not terrorists".
Over the past week, the online forum has attracted more than 590 Israelis signing up to repeat Ms Hammerman's act of civil disobedience.
"That has really surprised and encouraged me," she said. "I did not realise there were so many other Israelis who have had enough of this outrageous law."
Still, the coverage of Ms Hammerman and her supporters in the Israeli media has been largely hostile. During a television interview last week, she was accused of endangering Israelis with her trips. The show's host, Yaron London, asked whether she had inspected the Palestinian women's underclothes for explosives before allowing them into her car.
She will will not be deterred, though. She said the group had discussed future trips for Palestinians, including taking them to pray at al-Aqsa, the mosque in Jerusalem that has been inaccessible to most Palestinians for at least a decade, and visits to Palestinian relatives they cannot see in Jerusalem and Israel.
"We need to get Israelis meeting Palestinians again, having fun with them and seeing that they are human beings with the same rights as us."
She said her immediate goal was to kick-start a discussion among Israelis about the legality and morality of Israel's laws and challenge the public's "blind obedience" to authority.
Ms Lyth added that the Palestinian women "who have gone on our trips are the heroes of their village. They and their families know they are taking a big risk in breaking the law, but harassment is part of their daily lives anyway".
Till now the trips have been restricted to smuggling Palestinian women and children only, said Ms Hammerman. "It is harder to bring men in without being discovered and the authorities would be likely to treat Palestinian men much more harshly if they were caught."
A version of this article originally appeared in The National (http://www.thenational.ae), published in Abu Dhabi.
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