CARACAS—Venezuela’s central bank and the most prominent website publishing information on the country’s currency black market are squaring off in U.S. court where this South American government is seeking the closure of the outlet it blames for destabilizing its entire economy.

Lawyers for Delaware-registered DolarToday.com on Thursday filed a motion to dismiss the lawsuit submitted by President Nicolás Maduro’s embattled leftist administration in October, in which it accused the site of engaging in cyberterrorism and manipulating...