Last year, Erdogan vowed to "eradicate" Twitter after allegations of government corruption were published on the micro-blogging site.
The proposed law, debated by a parliamentary commission on Thursday, would allow ministers to order access restricted to any website deemed to threaten lives, public order or people's rights and freedoms by committing a crime.
The Telecommunications Directorate (TIB) would have to comply within four hours, and then apply for a court order for the ban to be extended beyond 24 hours.
Communications Minister Lutfu Elvan this week defended the proposal, saying it was needed after Turkey's top court in October annulled previous legislation giving greater powers to ban websites, and saying it would only be used in emergencies.
Turkey came under international criticism for temporary bans on Facebook and Twitter as a corruption scandal unfolded last year. The opposition questioned the government's motives.
Erdogan said the corruption scandal was engineered by opponents in an attempt to topple him.
"Naturally the government will as a priority block sites and pages which it does not like and drag its feet on other ones," said Erdal Aksunger, an MP for Turkey's opposition CHP.
Twitter this week responded to a Turkish court order by blocking tweets from the account "Fuat Avni", which in recent months embarrassed the government with a series of leaks, including tip-offs on police raids on media outlets.
In a sign of the challenge Erdogan faces if he wants to effectively corral the Internet, a new Twitter account apparently from the same user sprang up hours later.
© Thomson Reuters 2015
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