The energy reform, which ended Pemex's decades-long monopoly, allowed Petróleos Mexicanos, as it is officially known, to keep most of its previous leases on the condition that it perform a minimum level of work on the fields.
The reform's fine print required all lease holders to invest in their projects within three years or risk losing them. Pemex was unable to comply due to several rounds of budget cuts, and the global oil price slump dramatically reduced its cash flow.
The energy ministry did not immediately respond to a request for comment.
Pemex is seeking a joint venture partner for its Maximino-Nobilis exploratory block in the Gulf of Mexico's deep waters, and has established a tie-up for its nearby Trion block with Australian mining and oil company BHP Billiton.
Three other exploratory leases face a legal challenge, and two more — one onshore and another in deep waters — were not granted the two-year extension, according to one of the sources.
The sources requested anonymity because they were not authorized to publicly discuss the matter.
The extensions give Pemex more time to execute minimum investment plans for the projects, but failure to do so would force it to return the acreage to the state for possible inclusion in future oil auctions.
Pemex was also given 286 extraction leases that are not affected by the investment requirement under the so-called Round Zero tender in 2014.
Since then, Mexico has conducted seven international oil auctions of onshore and offshore acreage that formerly belonged to Pemex.
The auctions have led to 70 new contracts that the energy ministry has estimated will bring $59 billion in new investment over the lifetime of the contracts.