Forecasters said sections of Portugal would see near hurricane-force winds, while parts of western Spain could be hit with tropical- force winds.
The remnants of Hurricane Leslie swept in overnight on Saturday, with winds gusting up to 176km/h (109mph).
Leslie was dubbed a "zombie" hurricane as it first formed on September 23, only to meander through the Atlantic Ocean for weeks.
Many across Hampton Roads were impacted by now post-tropical storm Michael, which was a tropical storm when it crossed over Hampton Roads and northeastern North Carolina on Thursday.
Costa said that Saturday night would be a critical period, warning of the risks of flooding in coastal areas, downed trees and power and telecoms outages.
The worst-affected areas in Portugal were around the capital, Lisbon, and in the districts of Coimbra and Leiria.
But in the coastal town of Figueira da Foz, Leslie's wind speeds reached up to 170 km/h, state broadcaster RTP said.
Learn More About Mental Health Awareness in Teens with NAMI Sarasota
Dr Wendy Fernander, president of the Bahamas Pharmaceutical Association, stressed the importance of having good mental health . She said: "I have had my own experience with mental health issues which I only came to terms with at the start of 2018".
The A1, the main motorway running through Portugal, was temporarily blocked by a fallen tree, authorities said. "People were very anxious".
More than 15,000 homes were reported to be without power, while several flights to and from Lisbon were cancelled.
Some weakening is forecast during the next day or so, but Leslie is expected to transition into a powerful post-tropical cyclone by Saturday night, October 13.
Over the past 176 years, only Hurricane Vince has made landfall on the Iberian peninsula, hitting southern Spain in 2005, according to weather records cited by experts.
The system that was Hurricane Michael is now a strong North Atlantic low-pressure system speeding toward Europe.
Ophelia then made landfall in Ireland as a violent storm, killing three people.
Leslie moved east on Sunday across the Iberian Peninsula to Spain, where authorities issued warnings for heavy rains and storm conditions for the northern part of the country.