YEREVAN/BAKU (Reuters) - U.S. Secretary of State Mike Pompeo urged Armenia and Azerbaijan to pursue a diplomatic solution to the Nagorno-Karabakh conflict as fighting in and around the mountain enclave entered a second month on Tuesday, defying a ceasefire brokered in Washington.Armenia acknowledged overnight that Nagorno-Karabakh forces had withdrawn from a strategic town between the enclave and the Iranian border, an apparent military gain for Azerbaijan. Both sides accused each other on Tuesday of striking targets outside Nagorno-Karabakh itself in defiance of a truce brokered by Pompeo at the weekend. Pompeo, in India on Tuesday, spoke separately with Armenian Prime Minister Nikol Pashinyan and Azeri President Ilham Aliyev and “pressed the leaders to abide by their commitments to cease hostilities and pursue a diplomatic solution”, the State Department said. World powers want to prevent a wider war that might suck in Turkey, an ally of Azerbaijan, and Russia, which has a defence pact with Armenia. The conflict is also close to pipelines that carry oil and gas from Azerbaijan to international markets. Azerbaijan’s military gains could make a diplomatic solution more difficult: it rejects any solution that would leave Armenians in control of an enclave that is part of Azerbaijan but populated and controlled by ethnic Armenians. Armenia says it will not withdraw from territory it views as part of its historic homeland and where the population needs protection.