At the Jizake Dai Show of SSI in 2008, Kokushi Muso's Junmai Daiginjo (Takasago Shuzo) and Jozen Nyosui's Shinmai Shinshu (Shirataki Shuzo) received the first (platinum) prizes for the combination with tuna. This is a selection by sommeliers of the Sake Service Institute in Tokyo. In general, these colleagues of mine (I am also a sommelier certified by the SSI) advise a light and delicate sake for tuna. Tuna is fatty red meat and tastes stronger than white fish. The reason to drink this type of sake is that it refreshes the mouth, more than a fear to obliterate the taste of the fish. And both recommended sakes are indeed light: it is a characteristic of sakes both from Hokkaido (Kokushi Muso) and Niigata (Jozen Nyosui) to be very dry and light. On the same note, in the case of pairing with wine, I would recommend a very dry white wine or a light red wine.
But other types of sake fit as well. Red tuna meat has a certain sourness, so a sour Junmai made with the Yamahai-method would also fit, especially if drunk cold.
Otoro is fat and creamy, with little umami - in fact, rather like foie gras -, and its popularity is a relatively recent phenomenon in Japan. It is difficult to combine with both wine and sake. The most logical choice would probably be a cold Honjozo Reishu, to wash away the fatty taste. But Japan's top sommelier Tasaki Shinya (in: "Wa" no shokutaku ni niau osake, Chukoshinsho, 2010) in contrast also suggests an aged sake, like a sweet and nutty koshu. The same pattern is repeated in the case of wine: I would suggest either a very dry white wine, or a very sweet one made with the Sémillon grape.
It is a pity neither such sakes nor such wines are available in sushi shops, even in Japan, but you can try it out at home!