The state-controlled People's Daily reported the news early Sunday on its English Twitter feed, saying that the government's procurement agency "has excluded Symantec & Kaspersky" from a list of security software suppliers.
A second tweet said that government procurement office had approved the use five anti-virus software brands, all from China: Qihoo 360 Technology Co, Venustech, CAJinchen, Beijing Jiangmin and Rising.
Officials with Symantec could not be reached for comment.
Kaspersky spokesman Alejandro Arango said: "We are investigating and engaging in conversations with Chinese authorities about this matter. It is too premature to go into any additional details at this time."
The report comes after Beijing late last week updated a public website that lists technology vendors whose goods are approved use for use by the nation's massive central government. It was not immediately clear if agencies were being advised to avoid other non-Chinese products.
The report is the latest sign that Beijing is intent on promoting use of domestic information technology products after leaks from former National Security Agency contractor Edward Snowden raised concerns about foreign surveillance programs. Tensions between Washington and Beijing have also risen this year after the United States indicted Chinese soldiers on cyber espionage charges.
Symantec last month said it was in talks with authorities following reports that China had banned use of one of its products, data loss prevention software. At the time a Symantec spokeswoman said that there was no indication of a ban on the company's flagship anti-virus software programs.
The company does not break out sales in China. Revenue in its Asia Pacific region dropped 10 percent to $1.2 billion in its most-recent fiscal year, which ended in March.
Other U.S. firms including Cisco Systems Inc, International Business Machines Corp and Microsoft Corp have encountered challenges in China since Snowden began leaking documents about U.S. surveillance programs last year.
Chinese media reported in May that authorities had banned government use of Windows 8, the current version of Microsoft Corp's operating system for personal computers.
The official Xinhua news agency said the ban was to ensure computer security after Microsoft ended support for its Windows XP operating system, which was widely used in China.