Investors also remained cautious weighing the impact of government's demonetisation move. Surging US bond yields have also contributed to the rupee's fall.
Moreover, the US currency was trading at multi-year highs against its major rivals in overseas markets.
The rupee had hit its all-time intra-day low of 68.85 and closed at 68.80 on August 28, 2013.
Expectations that Trump will adopt an expansionary fiscal measures -- which will drive inflation higher and lead to higher US interest rates -- are behind surging US yields that have attracted investors towards the dollar.
Consistent dollar demand from importers mainly kept the rupee under pressure.
At the interbank foreign exchange market, the rupee opened lower at 68.76 a dollar against 68.56 previously and and dropped to an all-time intra-day new low of 68.86 in the afternoon trade.
The Indian currency has shrunk 2.92 per cent since Donald Trump's victory in the US Presidential polls earlier this month.
Sentiment was mainly hit by the dollar surging to multi-year highs against a basket of major global currencies on better prospects for hike in US interest rates, banks forex dealers said.
The benchmark BSE Sensex was down by 193.42 points, or 0.74 per cent, at 25,858.39 in afternoon trade.