By Thomas Escritt and Linda Sieg THE HAGUE/TOKYO (Reuters) - U.S. President Barack Obama brought together the leaders of Japan and South Korea for their first face-to-face talks as a North Korean ballistic missile launch underscored the need for Washington's two key Asian allies to repair their strained ties. Washington hopes the three-way summit will improve relations between Seoul and Tokyo, which are clouded by the legacy of Japan's 1910-1945 colonial rule of the Korean peninsula and Seoul's concerns that Prime Minister Shinzo Abe wants to rewrite Japan's wartime past with a less apologetic tone. The United States wants to strengthen the allies' combined response to regional concerns such as North Korea's banned weapons programs and China's growing assertiveness in disputed waters.