MOSCOW — The U.S. and Russia urged the governments of Armenia and Azerbaijan to end fighting around the separatist Nagorno-Karabakh region, after an outbreak of intense combat over the weekend claimed the lives of at least 30 people and injured many more.

Late Friday, Azeri forces launched a bid to seize positions in Nagorno-Karabakh, a predominantly ethnic Armenian enclave that lies within Azerbaijan’s borders and was overtaken by Armenia during a six-year war that ended with a 1994 cease-fire.