ISTANBUL—Turkey is stepping back from plans to toughen Internet censorship and will make it harder to ban access to websites, after the announcement of harsh new Internet laws triggered street protests and international criticism.

A plan to require Turkish Internet users to choose one of four state-mandated browsing filters starting this month has been scrapped, said Serhat Ozeren, head of the Internet Board at the Ministry of Transport and Communications, in an interview on Friday.

Instead,...