KARACHI (Reuters) - The Pakistani rupee fell sharply on Tuesday, hovering around its lowest ever levels amid increased demand for the dollar, which dealers said could weaken the rupee further in coming days. The rupee, which fell to its lowest ever closing of 84.90 to the dollar last week, closed at 84.62/68, weaker than the previous days close of 84.30/40. There were pretty heavy import payments today, which pushed the demand for the dollar much higher, said a dealer at a brokerage house. There are still some payments pending in the market, which means the rupee could ease further over the next day or two, he said. Dealers said dollar inflows from remittances have helped steady the rupee slightly in recent days, but consistent dollar demand from oil companies and other importers was still applying pressure, dealers said.