Exactly 60 years after the election of Brazil's first female MP, the country's first female president has promised to fight for women's rights with the battle cry: "Yes, women can."

Speaking after her historic election on Sunday night, Dilma Rousseff echoed US president Barack Obama's "Yes, we can" slogan, telling supporters: "Equal opportunities for men and women are an essential principle of democracy.

"I would like for fathers and mothers to look into their daughters' eyes today and tell them: 'Yes, women can.' I would like to register my first post-election commitment: to honour Brazilian women so that this unprecedented fact becomes a natural event."

Rousseff, 62, who was elected with 56% of the vote and became the eighth elected female president in Latin America and the Caribbean, will take office on 1 January. She added that she would fight for greater opportunities for women "in businesses, civil institutions … and in the whole of our society".

Brazil's incoming president is widely tipped to promote several women to government positions, among them Maria das Graças Foster, a director at Brazil's state-run energy company, Petrobras. Foster is rumoured to be in line either to take over as the company's chief executive or to head a ministry.

Marta Suplicy, São Paulo's former mayor and a woman that the local press call Rousseff's "first friend", was elected to Brazil's senate with more than 8m votes and will work closely with the new president.

Nilcéa Freire, the academic who led President Lula's special secretariat for women's policies, may also get a role.

Fátima Pacheco Jordão, a Brazilian sociologist, said Rousseff's allusion to the importance of women in democracy was a major advance that went beyond emotion and rhetoric.

"Most important in this feminist-tinged speech was that she described the advance of gender equality issues as one of the foundations of democracy," she said. "Never has a [Brazilian] president treated the gender question in this way."

Jordão said Rousseff's recognition of the "gender deficit" gave her hope that she would follow women-friendly policies such as those introduced by Chile's former president Michelle Bachelet, now head of UN Women.

"It is possible [Rousseff] may introduce specific policies that are better than Lula's without ever having promised them," she added.

Despite excitement over the election of Brazil's first "presidenta", most senior cabinet posts will still be occupied by men. "The proportion of women in politics in Brazil is very limited, worse than many Latin American countries and several in Africa," said Jordão, pointing out that Rousseff's campaign had focused on continuity not gender issues.

Whereas Obama's campaign slogan had been "Yes, we can", Jordão said Rousseff's could have been: "Yes – it's under control."