(Reuters) -   Russia's Wagner private army claimed on Saturday to have finally captured the eastern Ukrainian city of Bakhmut after the longest and bloodiest battle of the war, while Kyiv denied the city had fallen though it called the situation there critical.If confirmed, the announcement by Wagner leader Yevgeny Prigozhin that his troops had finally pushed the Ukrainians out of the last built-up area inside the city would amount to claiming Moscow's first big prize for more than 10 months.But any sense of victory for Russia appears likely to be fleeting. The announcement comes after a week in which Ukrainian forces have made their most rapid gains for six months on Bakhmut's northern and southern flanks, which Prigozhin has said put his troops inside the city at risk of encirclement. Prigozhin, who has repeatedly denounced Russia's regular military for abandoning ground captured earlier by his men, said his own forces would now pull out of Bakhmut in five days to rest, handing the ruins of the city over to the regular military.