The rupee fell 13 paise to 79.58 against the US dollar in early trade on Tuesday as strong American currency overseas and losses in domestic equities weighed on investor sentiments. Besides, persistent foreign fund outflows and elevated crude oil prices kept the pressure on the local unit, forex traders said. At the interbank foreign exchange, the rupee opened lower at 79.55 against the American dollar and slipped further to quote at 79.58, a decline of 13 paise over its last close.