Mr. Gelsinger has argued that government subsidies are crucial to bring the costs of building new factories in line with costs of setting up plants in Asia. He has lobbied officials in the United States and Europe about parallel subsidy packages that could include grants to set up new chip factories, stating that government support may determine how far and how fast Intel expands in both regions.

At the same time, Mr. Gelsinger and other Intel officials have held talks with officials in at least seven countries in Europe about a potential new site. Intel now has factories in Ireland and Israel, in addition to Arizona, Oregon and New Mexico.

Germany had seemed a strong candidate, partly because of the concentration of automakers that have become key customers for chip makers. Mr. Gelsinger spoke at an auto industry trade show in September in Munich, highlighting driver-assistance technology from Intel’s Mobileye unit and posting a photo fist-bumping with then-Chancellor Angela Merkel.

The country is no stranger to chip manufacturing. One major production hub is Dresden, where Infineon, GlobalFoundries and Bosch operate semiconductor factories. Magdeburg, in the state of Saxony-Anhalt, is about 150 miles northwest of Dresden and 100 miles west of Berlin.

“Two semiconductor factories by Intel in Magdeburg are an important and strong impulse for the economy in difficult times, and a central leap for the digital sovereignty of Europe,” said Robert Habeck, Germany’s economy minister.

In addition to the German factory, Intel said it would spend an additional €12 billion to double its manufacturing space in Leixlip, a town west of Dublin. In Italy, the company said it has entered into negotiations to build an advanced factory to package and test chips, with a potential investment of €4.5 billion and roughly 1,500 jobs.

In France, Intel said it would build a research and development hub, creating 1,000 jobs, that will focus on fields that include high-performance computing. In Poland, the company is expanding lab space.