The MPs, who were among the first four women to be elected to the country's National Assembly in May, have angered their Islamist colleagues, who say they say they are flouting sharia, or Islamic law.
One of the two is going further by demanding the scrapping of an amendment to electoral regulations that says they have to observe sharia in parliament.
The MPs' stand is part of a backlash against the fashion for stricter dress codes for women across the Arab world.
Last week, the rector of al-Azhar University in Cairo, traditionally the principal seat of Sunni Islamic learning, banned women students from wearing the face veil in women-only classes and student dormitories, and was followed by other academic institutions there.
Students at Khalifa University in Sharjah, the most conservative of the seven city-states that make up the United Arab Emirates, have also reportedly been told to stop wearing the veil, known in Arabic as the niqab.
In Kuwait, the issue has arisen as part of a campaign by Dr Dashti, one of the country's leading economists as well as a women's rights activist and politician, against what she regards as unconstitutional implementation of sharia. As with all four women MPs, she has a doctorate from the United States.
When electoral law was changed in 2005 to allow women in Kuwait to vote and stand for parliament, Islamists inserted a law-minute rider that "women as voters and MPs" would have to follow sharia.
It did not specify precisely where or how.