No-one was wounded in the shootings in the central commercial area of Bangkok, although five people were killed in weekend violence in the city and the eastern province of Trat, four of them young children.
National security chief Paradorn Pattanathabutr said: "Recently we have been seeing more incidents like this happening more frequently."
The protesters, whose disruption of a general election this month left polarised Thailand in political paralysis, want to topple Prime Minister Yingluck Shinawatra and erase the influence of her brother, ousted premier Thaksin Shinawatra, who is seen by many as the real power in the country.
Occasional contact between the two sides, amid calls for an end to the violence which has hit tourism and the economy, has so far led to nothing.
Demonstrators pushed against the wrought iron gates of the national police headquarters in Bangkok yesterday, demanding the proper investigation of more than 20 deaths since the beginning of the protests.