Faulty cells in some batteries could short-circuit and ignite, a spokesperson said.
Some 858 Taycans were initially identified as being at risk and recalled in January, but after further checks the company determined that further vehicles could also be affected.
Porsche said 2,936 of the sporty four-door cars showed "anomalies", which requires changing the modules on the 600-kilogram (1,300-pound) batteries housed under the car.
Another 4,522 Taycans have not been inspected and must be brought to repair shops for verification.
Renault, Ford and General Motors have all recently had to recall models due to defective batteries.
The cells for the Taycan's batteries are manufactured by Korea's LG, while the batteries themselves are assembled in Germany before being inserted into the cars at Porsche's Zuffenhausen factory.
Launched in 2019, the Taycan sold more than 40,000 units in 2023, up 16.7 percent from the previous year.
As Porsche's first electric model, it is key for the German brand, which expects 80 percent of its sales to be electric by 2030 as it gradually electrifies the rest of its range, from the small Macan SUV this year to the sporty 718 in 2025.
