WASHINGTON — The Justice Department is trying to force an internet hosting company to turn over information about everyone who visited a website used to organize protests during President Trump’s inauguration, setting off a new fight over surveillance and privacy limits.

Federal investigators last month persuaded a judge to issue a search warrant to the company, Dreamhost, demanding that it turn over data identifying all the computers that visited its customer’s website and what each visitor viewed or uploaded.

The company says that would result in the disclosure of a large volume of information about people who had nothing to do with the protests. Over 1.3 million requests were made to view pages on the website in the six days after inauguration alone, it said.

Dreamhost is fighting the warrant as unconstitutionally broad.

“In essence, the search warrant not only aims to identify the political dissidents of the current administration, but attempts to identify and understand what content each of these dissidents viewed on the website,” two lawyers for Dreamhost, Raymond Aghaian and Chris Ghazarian, wrote in a court motion opposing the demand.