Seven-year-old Halla Tómasdóttir was confused on her mother’s birthday in 1975. Her mother and aunts weren’t in the kitchen as usual, instead directing their husbands and brothers to do the work. That was because women were taking the day off to demonstrate their value to society amid Iceland’s first national women’s strike.

More than four decades later, Ms. Tómasdóttir is the country’s new president, nurtured by the message she absorbed on that day.

“They told me they wanted to show the world that they matter,” Ms. Tómasdóttir said this week. “I think that was the day I decided I might like to matter.”

Ms. Tómasdóttir, a feminist finance expert for whom the singer Björk campaigned, clinched the presidency and officially took the reins on Thursday from Guðni Jóhannesson, who stepped down after two four-year terms.

Iceland, a Nordic island nation with a population of about 380,000, operates as a constitutional republic with a parliamentary twist. The president, who is not required to be affiliated with any political party, serves as the head of state but wields mostly ceremonial clout. The real executive muscle lies with the prime minister, typically the leader who can command Parliament’s majority.

Still, Ms. Tómasdóttir intends to make a difference.

“My goal is not to be a president with all the answers,” she said. “I want to be a president that asks the right questions.”