The glass is called Valor Glass and is a "substantial improvement" in quality over existing products, he said. It has superior strength and is more damage-resistant, according to Corning.
Weeks said the companies have been working together for a number of years to improve pharmaceutical packaging.
When asked if the glass would have been produced overseas if the government hadn't been involved in the process, Weeks responded, "We probably would have taken a little more balanced approach."
He also said there were no incentives, like tax breaks, from the federal government to make the product in the U.S.
Weeks said what the Trump administration is doing is help streamline the process.
"You can't reindustrialize a major industry like this without touching the government at every level. We need our product to be approved by the FDA. We need our process to be approved by the EPA," he said.
"Then we need to work with governance both at states and international and national to make sure we are globally competitive and that's the help that the Office of American Innovation brought to us."
— CNBC's Stephen Desaulniers contributed to this report.