The process got under way last year and has already been completed in some districts, including Angyalföld and Csepel.
It is still ongoing in others, among them Zugló and Újbuda.
The modernisation is part of a national programme and has already seen the incumbent make internet access speeds of at least 30 Mbps available to an additional 464,000 households around the country.
A further 500,000 will be added this year, with funding for the modernisation being entirely from internal sources.
High-speed broadband services supplied by Magyar Telekom are already accessible to over 2.5 million households.