Turkey's main opposition party wants parliament to be recalled to adopt a new penal code in time for a key EU report on the country's accession bid.
The adultery clause triggered heated debate in Turkey
Voting on the Turkish penal reforms was suspended last week amid a row over a clause criminalising adultery.
The European Commission says the penal code must be changed before talks on Turkish membership of the EU can begin.
The Commission is due to report on 6 October on whether Turkey has met the criteria set by the EU.
The Commission's president-designate, Jose Manuel Durao Barroso, told the French newspaper Le Monde that Turkey was not yet ready for membership, but that if it met all the criteria "I don't see how we could say 'no'."
He insisted that "it is Turkey that has to adapt to the rules of the European Union, not Europe to Turkey's rules".
In Ankara, the leader of Turkey's opposition Republican People's Party, Deniz Baykal, called for the country's parliament to be recalled early, so as to vote on the reformed penal code.
If his call is heeded, then the new penal code could be law in time for the EU report's publication.
The BBC's Jonny Dymond in Istanbul says the commission has made it clear privately that it feels able to publish a report that is conditional upon the passage at a later date of the reformed code.
But the psychological impact would be important. If Turkey could get the code through parliament before the report, Ankara's EU campaign would perhaps regain some of the impetus it has so obviously lost over the past four days, our correspondent says.
Last week Turkish Prime Minister Recep Tayyip Erdogan hit out at the European Union, telling it not to interfere in his country's internal affairs.
He spoke after the European Commission warned that Turkey's bid to join the EU could be complicated by its delay in passing the penal code.
Mr Erdogan is due to visit Brussels this week to meet the leaders of the new European Parliament and try to ease fears about Turkey's eventual EU membership.
The reform bill was withdrawn on Thursday because of the adultery row.
The clause re-criminalising adultery is part of a package of proposed changes to overhaul Turkey's 78-year-old penal code. The reforms also include:
- Tougher penalties for convicted torturers. Torture in police stations and prisons would be punished with 12 years in jail
- Clauses on genocide, crimes against humanity and people-trafficking - the first time such crimes are mentioned in the Turkish penal code
- Stronger laws against rape and so-called "honour" crimes against women.