MEXICO CITY (Reuters) -Mexican President-elect Claudia Sheinbaum is set to prioritize public internet access after taking office, an adviser said on Wednesday.

Jose Merino, an adviser to Sheinbaum on digital strategy, told a telecoms conference in Mexico City that the state must reach areas of the country that private telecoms companies do not cover, underscoring her intention to continue outgoing President Andres Manual Lopez Obrador's unfinished project to bring internet to all Mexicans.

Sheinbaum won last Sunday's election by securing over half of the vote, according to preliminary results, and is set to take office on Oct. 1.

Merino said a sustainable national telecoms policy could be rolled out to address how frequency bands are auctioned and Mexico's lagging connectivity in the medium to long term as part of the new government's agenda.

"Denying access for any reason to a person's data and connectivity is denying them the ability to exercise a multitude of rights," Merino said.

Mexico's telecoms regulator, the IFT, was one of the institutions that Lopez Obrador had proposed eliminating through constitutional reform.

Sheinbaum has said she plans to continue Lopez Obrador's initiatives. Industry watchers, however, are waiting to see if she will push forward with eliminating the IFT, and how she will manage regulation of the sector, which includes major companies like America Movil and Televisa.

"Making (the IFT) disappear is not seen as the best idea because we come from a time when it did not exist and we already know what a (government) secretariat is like, changing people all the time and then there is no accumulated knowledge," Gabriel Szekely, chief executive of Mexico's National Telecommunications Association (Anatel), told Reuters after Merino spoke.

(Reporting by Cassandra Garrison; Editing by Valentine Hilaire and Deepa Babington)

By Cassandra Garrison