Forex traders said muted opening of domestic equities weighed on the rupee.
BSE Sensex closed 413.45 points, or 1.01 per cent, higher at its all-time high of 41,352.17.
Silver prices gained Rs 75 to Rs 45,610 per kg from Rs 45,535 per kg in the previous trade.
Analysts said raising of bets by participants kept crude prices higher in futures trade here.
Forex traders said market participants were enthused following positive developments on the US-China trade talk front.
The 30-share Sensex rose 203.40 points or 0.50 per cent to 41,142.12 in morning session.
Losses in FMCG, auto, energy and select banking stocks eroded the gains with Sensex settling 70.99 points down at 40,938.72.
Silver prices gained Rs 234 to Rs 45,460 per kg from Saturday's close of Rs 45,226 per kg.
After starting significantly higher, the Sensex pared gains to trade 15.33 points or 0.04 per cent up at 41,025.04.
Forex traders said the weakening of the US dollar vis-a-vis other currencies overseas also supported the rupee.