The United States has established diplomatic relations with Montenegro.
The State Department said Tuesday the agreement came in an exchange of letters between President Bush and Montenegrin President Filip Vujanovic.
The State Department says it welcomes Montenegro's commitment to be an active and responsible member of the international community.
It also says it is pleased to see Serbia and Montenegro working in good faith to peacefully implement the end of their union.
Montenegrins voted in May to split from Serbia and establish independence.
The decision broke up the last remaining union from the former Yugoslavia