TOKYO—U.S. robots will examine the containment vessel of Reactor No. 1 at the quake-hit Fukushima Daiichi nuclear complex on Tuesday, as officials suspect there are leaks to plug before the whole vessel can be filled with water in an operation to cool the pressure vessel it houses and keep fuel submerged.

Concerns also have grown about a possible leak in the spent fuel pool of Reactor No. 4, said Hidehiko Nishiyama, spokesman of the government's Nuclear and Industrial Safety Agency. The pool holds the most fuel rods among...