DSI chief Tarit Pengdith announced the plan on Monday after a meeting of DSI officials, prosecutors and officers from Metropolitan Police Bureau.
The DSI last month issued summonses for 33 protest leaders to acknowledge charges of violating sections 113, 116, and 215 of the Criminal Code, which include insurrection.
They were due to report to the DSI headquarters on Chaeng Watthana Rd by Jan 3 to acknowledge the charges, but all failed to show up without showing reasonable grounds, Mr Tarit said.
The protest leaders claimed they were too busy with the the protest movement or other errands during the New Year period, he added.
As a result, the meeting on Monday resolved to seek warrants for their arrest from the court, because they continue to commit offences. This included the planned attempt to shut down Bangkok on Jan 13, the DSI chief said.
DSI investigators will hold another meeting on Tuesday to finalise their case and submit it to the court on Wednesday, he said.