Defining a primary key: Customer numbers are unique only within a country but may be duplicated across different countries

I am facing the following problem: I have a table with customer information like the *customer number*, i.e. customerID set up as the primary key, and, besides a number of other data, also a country value in the form of a *country code*, countryID. However, customer data from other countries should also be imported into this table. Although the customer numbers are unique within a country, they are not cross-country. Customer numbers should not be changed for organizational reasons. How can a key still be ensured for each customer in this table?