Smoke blankets the capital Santiago as fiery protests rage while thousands also hit the streets of other major cities.

Santiago, Chile – Protesters in Chile rejected President Sebastian Pinera’s political concessions as major demonstrations continued across the country demanding greater equality and constitutional changes.

Central Santiago was covered in smoke on Tuesday evening as a fire raged by the hill in Santa Lucia during unrest against social inequality and police violence.

Thousands more gathered in the streets in cities across the country, from Puerto Montt in the south to Antofagasta in the north.

In the coastal town of Valparaiso, demonstrators gathered to the sound of banging pots after another volatile night during which police fired tear gas.

Protests erupted again on Tuesday despite Pinera’s decision to reshuffle his cabinet on Monday, as part of his moves to quell a weeklong uprising against his administration.

Pinera replaced one-third of his cabinet, including Andres Chadwick, the right-wing interior minister who was heavily criticised for calling protesters “criminals” last week.

Chadwick, who is Pinera’s cousin, was openly supportive of Augusto Pinochet‘s regime during Chile’s dictatorship that ended in 1990.

“Chile has changed and the government, too, has to change to confront these new challenges in these new times,” Pinera said as he announced the replacement of his cabinet, which also includes the finance and labour ministers.

“These measures won’t solve all our problems but they are an important first step. They reflect the firm will of our government and the strong commitment of each of us in favour of a socially more just and equitable Chile.”

But the cabinet changes fell flat as new protests erupted after the announcement.

What started as a demonstration against a four percent increase in Santiago’s metro rail fare earlier this month has evolved into a wider dissent against decades of growing inequality.

Many protesters say they are angry with the “neoliberalism” that has led to poor public services, including the almost complete privatisation of pensions, health and education.

Call for new constitution

Others are demanding a new constitution, which remains as a hangover of the Pinochet regime.

Demonstrators clash with riot police during protests against the government economic policies, in the surroundings of the Moneda presidential palace in Santiago [Pedro Ugarte/AFP]

“A new constitution is the only way. All the past governments couldn’t change the constitution, and this is what we need. The Chileans are clear,” Patricia, a 62-year-old protester in Santiago, told Al Jazeera, adding she struggled to survive on her stagnant salary.

“The repression has to change because this social movement isn’t going to stop.”

On Tuesday afternoon, a peaceful march formed in Santiago’s Plaza Italia, while vandalism and looting took place elsewhere in the city.

Armed police fired water cannon at protesters gathered along the Alameda, the main highway leading towards the presidential palace.

One staff member of the national human rights institute, the INDH, was wounded by armed forces during the clashes.

The incident took place following the arrival of rights watchdog Amnesty International to investigate allegations of human rights violations against the demonstrators. The UN Human Rights Commission will also send a team to Chile this week.

“Even though the eyes are on Chile, the president hasn’t stopped the repression on the streets, and mobilisation continues to be massive,” Amnesty’s America director Erika Guevara told Al Jazeera.

“The demonstrators are not seeing genuine commitment from the government to really address their demands.”

Allegations of rights abuses

At least 20 people have died since the unrest began.

Currently, 3,712 are detained and the INDH has filed 138 judicial cases of alleged violence, including sexual harassment and other forms of abuse.

Pinera has pledged full transparency in the investigations, and lifted the state of emergency that granted the state special powers to control the right to assembly and movement.

“It’s quite clear there have been instances of human rights violations – if the reports are true about the nature of the injuries, and the video evidence,” said Saladin D Meckled-Garcia, senior lecturer in the department of political science at University College London.

“People are unhappy and an authoritarian government that seems to respond with violence isn’t going to solve it.”

Opposition parties are reportedly working on a proposal to change the constitution, and are expected to present on Wednesday a case against Chadwick, the former minister of the interior.