With the press of a button on a computer keyboard, Commerce Secretary C. William Verity yesterday sent an export license humming electronically across the country -- part of a major effort to make it easier for U.S. high-technology companies to sell overseas.

The new electronic system for issuing export licenses, unveiled yesterday by the Commerce Department, will cut to three days the time it takes to check whether a product can be shipped overseas without harming U.S. national security. Before the electronic system went into effect, it took 13 days to win license approval on sales to non-Communist nations; in 1954 the approval time was as long as 54 days.

The Commerce Department had been accused by business groups of costing them high-tech sales because of the time it took to get export licenses. These charges led to an effort in the past four years to upgrade the licensing procedure while tightening the net to ensure that overseas sales that could harm national security do not slip through.

The license issued yesterday went to Hewlett-Packard Co. of Palo Alto, Calif., and was for the sale of a $12,000 computer to an Italian firm.

In a test of the operation last week, Perkin-Elmer Corp. of Norwalk, Conn., got its license in three days to sell a $108,000 patient monitoring system to a French hospital. "We got immediate turnaround -- three days compared to seven to 10 days," said Norman W. Smith, Perkin-Elmer's director of trade controls.

His company jumped in early, working with Commerce Department officials to develop the software needed to hook into the electronic system.

"It will improve our response to customers and gives predictability to licensing," said Smith, a member of the subcommittee on export administration appointed by the President's Export Council.

The new system allows applicants for export licenses to non-Communist countries, which cover 80 percent of all requests, to file their applications electronically. The application is screened by a computer to check if the product is eligible for a license and if the buyer or seller has a record of diverting high-technology products to Soviet bloc nations. A licensing agent double-checks the computer, and the license is approved or denied within three days. This speedup will reduce the agency's paperwork, thereby cutting the time it takes to handle license applications for China and Eastern bloc nations and the Soviet Union, which face stricter criteria.