Fresh clashes broke out between Azerbaijan and ethnic Armenian forces over Nagorno-Karabakh - a day after talks in Washington were held in an effort to end the bloodshed. Azerbaijan's defense ministry reported conflict in and around the mountainous breakaway region - considered part of Azerbaijan but populated and controlled by ethnic Armenians. It said that some areas had come under rocket and artillery fire from inside Armenian territory. In Nagorno-Karabakh, local officials accused Azerbaijan's forces of firing missiles into residential buildings in Stepanakert, the largest city in the region, which they deny. U.S. Secretary of State Mike Pompeo had separate discussions with the foreign ministers of both countries to try to put a stop the deadliest fighting in the Nagorno-Karabakh enclave in more than a quarter of a century. The collapse of two Russia-brokered ceasefires had already dimmed the prospect of a quick end to fighting - which broke out in September. Azeri forces say they have made territorial gains, including full control over the border with Iran. Armenia denies this. Nagorno-Karabakh's ethnic Armenian administration says its forces have repulsed attacks. Russian President Vladimir Putin said the month-long conflict may have killed as many as 5,000 people.