TOKYO—Bank of Japan Gov. Haruhiko Kuroda gave the green light for stocks to keep climbing Friday, saying the upward momentum is fueled by record-breaking profits, after the market value of Tokyo shares topped its 1980s bubble-era peak.

“At this moment, we don’t see any indication that the expectations in asset markets or of financial institutions are growing unduly or are excessively bullish,” Mr. Kuroda said.

The...