In the first quarter of last year, the Sunday Times was ranked third-most influential agenda-setting medium, the Mail & Guardian was second, and City Press first.
The Sunday Times came out tops for the first quarter of this year, followed by City Press and the Mail & Guardian.
The study tracked which media were most frequently quoted by their peers.
"What is heartening is the increase in quotes for South African weekly newspapers as opposed to international print, which suggests that local media have taken back the lead on local stories," Media Tenor managing director Theresa Lotter said in a statement.
While the Mail & Guardian broke the story on upgrades to President Jacob Zuma's Nkandla home, the Sunday Times and City Press continued to produce fresh angles on the story in the build-up to Public Protector Thuli Madonsela's report on the matter.
Beeld retained its position as most influential daily newspaper, but faced growing competition from The New Age.
"Beeld's niche coverage on domestic crime and societal issues saw Beeld reach top-three status in 2012 and the paper has continued, since then, as a highly influential medium," Lotter said.
The top three agenda-setting newspapers gave the ANC and its national executive committee coverage amounting to about half of their respective representation of political parties. Coverage of the Economic Freedom Fighters was 11% across each of the three newspapers.
The Sunday Times gave 27% representation to the DA and 13% to other political parties.
The City Press and the Mail & Guardian each gave 17% of their political coverage to the DA, with other parties accounting for 19% and 14% respectively.