Recep Tayyip Erdogan's Justice and Development Party and the Nationalist Action Party had agreed that scarves should be tied loosely with a knot beneath the chin, leaving the face exposed.
The government said on Friday that it was seeking suggestions on permissible styles for female students.
The main opposition Republican People's Party does not have enough seats to stop the measure but said it would appeal to the constitutional court to try to cancel it.
And in a second protest within a week, tens of thousands of flag-waving secular Turks were to hold a demonstration against the measure in Ankara on Saturday.
Head covering
Once the constitutional amendments are passed, the government plans to change laws governing higher education to specify what type of head covering will be allowed, to ensure that students do not attend classes in full-length chadors or burqas.
Islam and secularism are long-standing rivals in modern Turkey, founded by Mustafa Kemal Ataturk in 1923.
Ataturk sought to eliminate religion's place in a society with a 99-per cent Muslim population by banning religious garb and changing the alphabet from the Arabic to the Latin.
Secularism became a deeply ingrained ideology.
General Yasar Buyukanit, chief of the military, said last month the military's views on the headscarf issue are well known by the public.
The military leads the forces committed to preserving the staunchly secular principles of modern Turkey and has stepped into politics before.
Public backing
Erdogan, who won 47 per cent of the votes in general elections last year, has strong public backing and insists that his party is loyal to the secular traditions.
The government says the measure is aimed at expanding democracy and freedoms to progress the country's EU membership bid.
But secularists harbour deep suspicions about the real intentions of Erdogan - who had tried to criminalise adultery before being forced to step back by the EU.
Many secular women fear that allowing headscarves in universities will lead eventually to their being pressured to cover their bodies as well.