The rupee pulled back from one-week high hit earlier in the session on growing concerns other key allies of the government would withdraw support from the ruling coalition after the withdrawal of the Dravida Munnetra Kazhagam (DMK) party last week.
The rupee was last trading at 54.170/175, compared with the day's high of 54.06, which had marked the lowest since March 19.
The rupee closed at 54.33/34 on Friday. Hopes of more capital inflows following easing of foreign investor rules in debt, and positive global sentiment after Cyprus clinched a last-ditch deal aided the rupee in early trades.
The euro rose on Monday after Cyprus clinched a deal with international lenders for a 10-billion-euro bailout aimed at saving the country from financial meltdown.