last Friday's close of 165-167 paise.
Far-forward contracts maturing in November strengthened further to 317-319 paise from 309-311 paise.
The RBI has fixed the reference rate for the US dollar at 54.5610 and for euro at 71.0815.
The rupee also fell back against the pound sterling to 87.96 from last weekend's close of 87.09 and also dropped to 71.35 per euro from 70.62.
It plunged against the Japanese yen to 66.71 per 100 yen from last close of 65.63.