In early trade on Monday, the Sensex crossed the 65,000 threshold for the first time.
The Sensex increased by 289 points to 65,008, setting a new record.
Nifty gained 87 points as well, reaching a record high of 19,276.
The Nifty Auto index also saw an increase, rising by 0.66 percent and setting a new high. The Nifty Bank index, which has significant weight, also hit a record high, contributing to the market's overall upbeat mood.
On the Nifty 50, HDFC, JSW Steel, Grasim, Eicher Motors, and HDFC Bank were the top five gainers. On the other hand, Power Grid Corporation, HDFC Life, Maruti, Sun Pharma, and UPL were the top losers.
The rise in Indian stocks follows gains on Wall Street and signs of easing inflation in the United States.