Rupee and bonds plunged following Reserve Bank of India Governor Urjit Patel's unexpected resignation after market hours on Monday shocked investors.
Concerns about likely mixed results from crucial state elections later on Tuesday also kept traders wary.
The rupee came off earlier lows at 72.1350 to the dollar after opening at 72.46, but was sharply lower from its close of 71.35 on Monday.
The 10-year benchmark bond yield rose to 7.64 per cent from 7.59 per cent at the previous close.
The broader Nifty opened down 1.3 per cent but recovered some of its losses and was 0.9 percent lower.
Investors will await state election results for further trading cues during the day.
The RBI governor resigned abruptly after a months-long tussle over policy with the government that has raised concerns about the central bank's independence as a national election nears.
On Monday, the rupee weakened by 50 paise or 0.7 per cent against the dollar to 71.32.