WASHINGTON—The U.S. and Cuba will meet for a second round of diplomatic talks on Friday, indicating that the process of normalizing relations is moving ahead for now, despite significant hurdles to come.

Much as with the talks in Havana in January, the new round, in Washington, will focus on nuts-and-bolts issues related to establishing full-fledged embassies, the movement of diplomats, visas, access to equipment and banking.

While...