SEOUL — Prime Minister Shinzo Abe of Japan reached out to South Korea’s incoming president, Park Geun-hye, on Friday by sending a special envoy to Seoul with calls for mending ties that had become strained under their predecessors.

But no immediate breakthrough was expected as the two main East Asian allies of the United States exchanged barbs couched in diplomatic language, a reflection of their differences rooted in Japan’s often brutal colonial rule of Korea from 1910 until 1945.