A 34-year-old man killed 10 people on the streets of Cetinje before being shot dead by a passerby, officials said. They said it was unclear what had provoked the attack.
On Fox News, the president answered a hypothetical question about an attack on member Montenegro by wondering aloud about the alliance's founding agreement that "an attack on one is an attack on all."
An unidentified man threw a hand grenade at the compound in Podgorica before reportedly killing himself with another explosive. U.S. citizens are being asked to avoid the area until further notice.
In February, Montenegro's special prosecutor announced that "Russian state bodies" had backed a plot to overthrow the government and kill the prime minister. A trial is expected to begin this fall.
Russian officials responded by announcing plans to halt joint projects with the small Balkan nation. The last countries to join NATO were Balkan states Albania and Croatia, in 2009.