The company’s origins in Russia have for years fueled suspicions about possible ties to Russian intelligence agencies. Kaspersky denies the allegations.
Ms. Napolitano, the homeland security secretary under President Obama, signed the memo creating DACA and now is president of the University of California system.
The contracts are the latest step in President Trump’s bid to build a wall along the border with Mexico, a central campaign issue for him.
A divisive figure who rose to national attention last year during the Republican National Convention, Mr. Clarke previously said he had been offered a Homeland Security post.
The Department of Homeland Security awarded contracts to four companies for concrete wall prototypes to be built in the San Diego area.