SAO PAULO — President Dilma Rousseff on Friday admitted that Brazil must do "many things a lot better" in an address to a nation rocked by two weeks of mass protests over the cost of staging the 2014 World Cup and the need for better public services.

"We can do many things a lot better in Brazil," said Rousseff, a day after more than one million people marched to demand better living conditions, cheaper transport and more investment in education and health as well as a tougher fight against endemic corruption.

"People have a right to criticize," added Rousseff saying she would staunchly defend that right.

In an appeal for unity Rousseff, who promised to meet with the leaders of peaceful demonstrations as well as workers and community leaders, went on: "I am the president of all Brazil. Of those who support the demonstration and those who do not."

Reaching out to those who feel the government should direct more money to public services rather than on hosting major sporting events, she insisted that "football and sport are symbols of peace and peaceful coexistence."

But she added she would not stand by if demonstrations turned violent, as has been the case in several cities hit by cases of looting and attacks on public buildings including the foreign ministry and several government offices.

"The government cannot stand by as people attack public property . . . and bring chaos to our streets," she stressed.

"We need to inject oxygen into our political system, and make it more transparent and resistant" to the tough challenges facing a countries marked by extreme disparity between rich and poor," said Rousseff.

But she insisted that "we cannot put up with violence."

Brazil's first female president, who was jailed and tortured during the 1964-1985 military dictatorship, admitted nonetheless that her government had to "learn important lessons" from the wave of popular frustration which has seen tens of thousands of people march in more than 100 cities across the giant country of 200 million people.

She promised to devote profits from Brazil's lucrative oil sector to improving education, and said she would be meeting with local government leaders to address the issue of how to improve chronically under-invested public services, in particular public transport.

Before the Confederations Cup began on June 15 in Brasilia, demonstrators had marched in Sao Paulo and Rio de Janeiro in protest at rises in public transport fares already higher than in many major European cities.

But the protests have since spilled over amid popular anger at the billions of dollars being spent on the cost of staging two major football tournaments and the 2016 Rio summer Olympics.