Maximum sustained winds in the former Category 1 hurricane decreased to 70 miles per hour (110 kph) as the storm neared Portugal's west coast, the U.S National Hurricane Center in Miami said. If the storm drops to 74 maximum sustained winds, it would be downgraded to a tropical storm.
As of Saturday afternoon, Leslie was about 200 miles (320 km) west of Lisbon, the NHC said, adding that it is expected to become a post-tropical cyclone and dissipate by Sunday night or Monday.
Hurricane Leslie was quickly heading toward Portugal and Spain on Saturday, with forecasters expecting it to bring heavy rains and risky winds and surf to parts of the Iberian Peninsula.
Leslie is now over northern Spain, and emergency services warned of the possibility of flash floods and urged to motorists to be vigilant in case of strong winds.
Luis Belo Costa of Portugal's National Protection Agency recommended that people "avoid at all costs walking on the street". Forecasters said the swells are likely to bring "life-threatening surf and rip current conditions".
The government of Portugal has discontinued the tropical storm warning for Madeira Island.
Hurricanes formed on the American side of the Atlantic rarely bring their destructive force to Europe.
It is rare for an Atlantic hurricane to reach the Iberian Peninsula, and it is thought this could be the most powerful to hit Portugal since 1842.
Leslie first became a sub-tropical storm almost three weeks ago on September 23.
At least seven people were killed by the storm in Florida, Georgia and North Carolina from falling trees and other hurricane-related incidents, according to state officials.