To help shore up capital ratios, the Reserve Bank has allowed lenders to expand their base under the upcoming Basel III rules.
Additionally, there were some reassuring words from Finance Minister Arun Jaitley himself, who pledged all possible support to keep banks in "good health".
Asia ruled in the green after a raft of solid economic data in the US, which pushed up buying activity further.
The gauge had posted its biggest single-day gain of 777.35 points in almost 7 years in yesterday's trade.
It has gone up by over 1,240 points, posting its best two-day gains in almost seven years.
The NSE Nifty 50 index settled at 7,368.85, up 146.55 points, or 2.03 per cent.
The big positive was the government's commitment to its fiscal deficit target, raising expectations of a policy rate cut by RBI any time this month, traders said.
The rupee was another sentiment booster as it gained 31 paise to end at a 7-week high of 67.54 per dollar.
"The post-Budget rally extended for yet another day, with banks leading the pack after RBI eased capital regulations to meet Basel III norms. It also helped that FIIs were seen as buyers yesterday, putting a pause to their continuous sell off from Indian equities," said Anand James, Co-Head Technical Research Desk, Geojit BNP Paribas Financial Services.
Shares of state-owned banks such as SBI, PNB, Bank of Baroda were at the centre of buying activity.
Gains in Adani Ports, Hero MotoCorp, BHEL, Tata Steel, Axis Bank, NTPC, HDFC and Maruti Suzuki drove the upside.
As many 23 stocks gained while 7 lost.
Among sectors, the BSE realty index jumped most by rising 5.05 per cent, followed by banking (4.92 per cent), infrastructure (2.84 per cent), PSU (2.57 per cent), IT (2.49 per cent) and power (2.13 per cent).
The broader markets too continued to trend firm as retail investors boosted their bets, with the BSE small-cap index rising 2.21 per cent and mid-cap 1.88 per cent.
The market breadth remained positive as 1,970 stocks
ended higher and 693 closed lower while 131 ruled steady.
The total turnover dropped to Rs 3,356.08 crore, from Rs 4,723.03 crore yesterday.
"Market had taken faith in the Budget and believes that the worst is over. Investors expect a positive direction for the market this month aided by ECB and Fed policy meet. A sign of recovery in global market has raised optimism among participants," said Vinod Nair, Head-Fundamental Research, Geojit BNP Paribas Financial Services.
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