WASHINGTON/HAVANA — The U.S. Treasury Department on Tuesday announced regulatory changes to allow more American financial support for Cuba’s nascent private sector and bolster access to U.S. internet-based services, limited but timely measures that officials said would help give the island’s budding small businesses a leg up.

The United States said it would permit small entrepreneurs on the Communist-run island to open and access U.S. bank accounts from Cuba for the first time in…