The other banks include Axis Bank, Canara Bank, IDBI Bank, and Bank of Baroda New Zealand (BOB NZ), a Fitch release said.
Fitch has also retained its rating on the state-run Indian Bank at 'BB+'.
Retaining the ratings, Fitch said that the banking sector faces a challenging economic environment, although the new government's clear electoral mandate gives it the ability to pursue far-reaching economic reforms.
Uncertainties and risks remain in implementing key policies necessary to achieve the government's growth and fiscal deficit targets, the release said.
While retaining the ratings, Fitch said the viability eatings (VRs) of SBI, ICICI Bank and Axis Bank are at the same level as their IDRs and thus act as drivers for their long-term ratings, the release said.
SBI, ICICI Bank and Axis Bank are the only banks among Fitch's rated domestic banks to have investment-grade VRs of 'BBB-', reflecting their superior stand-alone credit profiles.
SBI, whose financial metrics are not as strong as ICICI Bank and Axis Bank, benefits from its large scale and status as a quasi-sovereign entity, which results in a solid funding profile and strong access to capital markets.
The VRs of Bank of Baroda, Canara Bank and Punjab National Bank are rated one notch lower at 'bb+', although Bank of Baroda's performance has been better than the other two in terms of capitalisation and exposure to stressed business sectors.
Capital buffers, or mandatory capital that financial institutions are required to hold in addition to other minimum capital requirements, for all three banks remain stretched, particularly at Canara Bank and Punjab National Bank, which was a key factor in VR downgrades of all three banks in 2013 and 2012, the release said.
Punjab National Bank's capital buffers are thinner compared with its stressed assets stock of around 15 per cent of total assets, the highest among the rated banks. The bulk of the stressed assets are restructured loans, the release said.