Investors are particularly keen on knowing who the country's new finance minister is -- likely to be ex-Commerce Minister Arun Jaitley, who is seen as the only obvious candidate for that role, according to two sources in the ruling party.
Indian shares ended flat in a volatile session, giving up earlier gains of nearly 2 percent due to profit-taking in blue-chips such as IDFC while caution ahead of Modi's ministerial appointments also weighed.
"We could see the pair target a high of 59.27-30 levels this week. We have the GDP data this week, but that is likely to be ignored. Market will be watching Modi and his team for cues," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
The partially convertible rupee closed at 58.71/72 per dollar compared to 58.52/53 on Friday. The unit moved in a wide band of 58.41 to 58.93 during the session. The rupee dropped 0.3 percent on the day, in its biggest single-day fall since April 23.
Dealers said the central bank was spotted buying dollars via state-run banks after the rupee touched session highs while it was also actively intervening in the forwards market.
In the onshore forwards, the one-year forward premium rose to as much as 471.75 points from 463.25 points at previous close while the six-month premium rose as high as 249 points from 243.50 points.
In the offshore non-deliverable forwards, the one-month contract was at 58.93 while the three-month was at 59.51.
FACTORS TO WATCH
* Euro roughly flat after Eurosceptic surge
* Stocks support Asia FX in thin trading
* Bonds, stocks brush off Eurosceptic election gains
* Foreign institutional investor flows
* For data on currency futures