RNA - Maha and Wafa al-Subaie, who are seeking asylum in Georgia after fleeing their family, said Absher - a government e-services app - was bad for women as it supported Saudi Arabia's strict male guardian system, Al-Jazeera reported.
"It gives men control over women," Wafa, 25, said. "They have to remove it," she added, referring to Google and Apple.
Absher, which is available in the Saudi version of Google and Apple online stores, allows men to update or withdraw permissions for female relatives to travel abroad and to get SMS updates if their passports are used, according to researchers.
Neither company was immediately available to comment. Apple's chief executive Tim Cook stated in February that he had not heard of Absher but pledged to "take a look at it".
A free tool created by the interior ministry, Absher allows Saudis to access a wide range of government services, such as renewing passports, making appointments and viewing traffic violations. In Apple's app store, it is listed as a productivity tool.
Saudi women must have permission from a male relative to work, marry and travel under the conservative Islamic kingdom's guardianship system, which has faced scrutiny following recent public cases of Saudi women seeking refuge overseas.
The al-Subaie sisters, who stole their father's phone to get themselves passports and authorisation to fly to Istanbul, noted that they knew of dozens of other young women who were looking to escape abusive families.
Tech giants could help bring about change in Saudi Arabia if they pulled Absher or insisted that it allows women to organise travel independently - which would significantly hamper the guardianship system - they said.
"If (they) remove this application, maybe the government will do something," Wafa told the Thomson Reuters Foundation in an interview.
The sisters' plea added to growing calls from rights groups, diplomats and US and European politicians for the app to be removed from online stores.
United Nations human rights chief Michelle Bachelet stated on Wednesday that she had asked tech companies in Silicon Valley "tough questions" this month about the "threats" posed by apps like Absher which allow Saudi men to restrict women's movement.
"Technology can, and should, be all about progress. But the hugely invasive powers that are being unleashed may do incalculable damage if there are not sufficient checks in place to respect human rights," she said in a statement.
Saudi Crown Prince Mohammad bin Salman has introduced reforms, such as lifting the driving ban for women, and indicated last year that he favoured ending the guardianship system. But he has stopped short of backing its annulment.
Western criticism of the kingdom has sharpened with the trial of 11 women activists who said last month that they had been tortured while in detention on charges related to human rights work and contacts with foreign journalists and diplomats.
The public prosecutor has denied the torture allegations and announced that the women had been arrested on suspicion of harming Saudi interests and offering support to hostile elements abroad.
A Saudi teen won global attention and asylum in Canada when she holed up in a Thai airport hotel in January to escape her family. Two other Saudi sisters who hid in Hong Kong for six months were granted visas in March to travel to a third country.
"Increasing cases of women fleeing the country are indicative of the situation of women in Saudi Arabia," Lynn Maalouf, Middle East research director for rights group Amnesty International, stated, adding, "Despite some limited reforms, (they) are inadequately protected against domestic violence and abuse and, more generally, are discriminated against."