He said: "There is no such problem in Western societies, but there is a problem in Turkey and I believe it is the first duty of those in politics to solve the problem."
The wearing of the hijab in universities was first banned shortly after a 1980 coup by military officers who viewed Islamists as a serious threat.
But the implementation of that rule varied during the law's early years.
Erdogan's apparent desire to include in the constitution an easing of the ban on the hijab in universities has predictably alarmed the secular elite.
The latter views the hijab as a symbolic threat to the separation of religion and state.
A copy of the first draft published by Turkish media includes alternative wordings for a possible article that would allow the hijab to be worn on campuses.
|The wearing of the hijab in universities was|
banned after a 1980 military coup [EPA]
University rectors and the head of Turkey's court of appeals both warned on Wednesday against any change in this regulation.
The head of Turkey's Higher Education Board - a well-known secularist law scholar - condemned Erdogan's move to lift the headscarf ban.
Erdogan Tezic said: "It is our mission to remind the public that any constitutional regulation that would abolish restrictions on clothing is illegal."
Ayse Ayata, a professor at Ankara's Middle East Technical University, said: "The lifting of the ban could lead to increased community pressure on uncovered women to cover up."
Erdogan on Wednesday rejected criticism that his governing Justice and Development (AK) party wanted to impose its own constitutional text on Turkey and pledged full, open discussions in parliament, the media and elsewhere.
The new constitution would replace a document that dates back to a period of military rule in Turkey in the early 1980s.
He said: "It's time to have a modern constitution that represents our nation's common sense and wisdom ... that will realise the ideal of a free Turkey."
But Ayata argued that the draft text risked eroding Turkey's system of checks and balances by giving parliament and the government too much power.
The AK party, which won a five-year mandate in July elections, says the new charter would favour the individual over the state and bring Turkey more into line with the European Union, which Ankara hopes to join.
|The secular elite failed to stop Gul from|
becoming president in August [Reuters]
Turkey's army, which views itself as the ultimate guarantor of secularism, is closely following the constitutional debates, as are nervous financial markets.
Ten years ago, the military ousted a government it saw as too Islamist.
In April, the army tried to stop the AK party's Abdullah Gul from becoming president in an election in parliament because of his Islamist roots and his wife's hijab.
Gul finally became president in August after the standoff with the army triggered early parliamentary elections which the AK party won resoundingly.