Saudi Arabia backed down under pressure from the U.S. and allowed Pakistan to be placed on an international terror-financing watch list, officials from countries involved in the decision said Friday, dealing a blow to the South Asian country’s struggling economy.

The Financial Action Task Force’s decision to put Pakistan on a list of countries with lax controls over terror financing and money laundering is part of a push by the Trump administration to punish Islamabad over what it sees as inaction against terrorists operating...