"In essence the threats were related to getting the music off the Internet or they were going to kill her," Martinez said.
"We can't validate how serious they are, but we do take it seriously," he said.
Martinez said officers were "keeping an extra eye out" for Black as they investigated the messages, which were made through her Los Angeles-based production and management companies.
One of the death threats was made by phone and the other by email, he said.
Martinez said that investigators had not yet identified the person or persons behind the threats, but that they could face criminal charges.
"We're going to investigate and determine, number one, the source of the comments and then based on the investigation determine what intent was and where we go from here," he said. "If we believe they were actually intended as threats we will work toward prosecution"
Black was an unknown Southern California middle school student before "Friday" was released in February by a boutique record label.
The video, in which Black can be seen singing gleefully about her weekend plans and riding in a car with friends, generated more than 110 million views on YouTube even as it was mocked by Internet critics.
Since then Black has made appearances on national television and racked up chart entries in the United States, Britain, Australia and Canada.
Visible Measures, a company that tracks the performance of Web videos, has said that including copies of the video, spoofs and other versions available on hundreds of video sites, "Friday" has generated more than 200 million views surpassing Lady Gaga's "Born This Way" and Justin Bieber's "Pray."