The battery unit, Panasonic Energy, had previously said it aimed to decide on building the factory by the end of March.
But Panasonic Holdings CEO Yuki Kusumi said in an interview that a decision would be made only "when the timing is right".
"I keep telling people we need to think about thoroughly raising productivity before setting up a third location," he said on Friday at the company's Tokyo office.
The comments come amid signs of cooling demand for EVs in the United States that have prompted some automakers, including General Motors and Ford, to scale back production plans.
Panasonic Energy has a plant in Nevada and has broken ground on a second one in Kansas. In December it said Oklahoma - where it was previously exploring building a factory - was no longer a candidate site.
The unit expects the Kansas plant to take its annual auto battery capacity to 80 gigawatt hours (GWh) a year. It aims to raise that to 200 GWh by early 2031.
Kusumi said his main instruction to the energy unit was to prioritise boosting production volume from its existing investment over deciding on the site of the third plant. Given the human resources requirements of a new plant, Kusumi said it was generally better to have fewer production sites.
He added there was room to raise production capacity by improving processes such as machine maintenance and that time lags due to changing circumstances happen in any business.
While consumer demand for EVs is growing worldwide, it has cooled in key markets such as the United States and Europe, and is not as profitable as industry executives had anticipated.
Higher interest rates have pushed many EVs out of reach for middle-income consumers who are also waiting for cheaper models now under development.
Kusumi said Panasonic wanted the energy unit to improve its manufacturing so that it would generate profits without relying on the U.S. Inflation Reduction Act, which spurred a wave of investments in new EV battery plants there.
The IRA and other U.S. legislation provide incentives aimed at boosting domestic production of EVs, batteries and raw materials.