Prosecutors asked the Istanbul court to sentence editor-in-chief Can Dundar and Ankara bureau chief Erdem Gul each to one aggravated life sentence, one ordinary life sentence and 30 years in jail, the Dogan news agency said, quoting the indictment, AFP reports.
The report said that both Erdogan and his hugely powerful but low-profile ally, the head of the National Intelligence Organization (MIT) Hakan Fidan, are named as plaintiffs in the indictment.
Dundar and Gul were both placed under arrest in late November over the report earlier in the year that claimed to show proof that a consignment of weapons seized at the border in January 2014 was bound for terrorists in Syria.
Since then, they have both been held in the Silivri jail on the outskirts of Istanbul ahead of their trial, whose date has still yet to be announced.
In the indictment, they have been formally charged with obtaining and revealing state secrets "for espionage purposes" and seeking to "violently" overthrow the Turkish government as well as aiding an "armed terrorist organization", it said.
The penalties demanded by the prosecutors are significantly higher than had previously been expected.
The case has amplified concerns about press freedom under the rule of Erdogan, who had personally warned Dundar he would "pay a price" over the front-page story.