The Agreement for Social Peace and a New Constitution, announced early Friday, gives voters the chance to decide whether they want a new constitution and, if so, whether it should be drafted by members of Congress along with ordinary Chileans elected for that task or solely by a special constituent assembly made up of citizens elected to write the document.

The move seeks to placate demonstrators who have paralyzed the capital, Santiago, with marches, looting and wanton destruction of subways and other public property. Other cities have also been rocked by protests. At least 23 people have died, and damages have been estimated at $2 billion, tarnishing Chile’s image as a tranquil, prosperous country.

“This accord is a first step, but it’s a historic first step and fundamental to begin to build a new social pact,” Gonzalo Blumel, the interior minister, told reporters Friday at the presidential palace shortly after the agreement was reached.

Supporters of the current constitution, which was enacted in 1980 during the military dictatorship of Augusto Pinochet, say it has been the pillar for Chile’s robust economic growth. Critics say the constitution—the latest of three Chile has had over the past 180 years—is illegitimate because it originated under his iron rule. Those demanding a new one want it to enshrine the right to state benefits, such as health care and pensions.

Since the end of the Pinochet regime in 1990, Chile has carried out constitutional amendments that led to the creation of a constitutional tribunal, an independent attorney general’s office, and other changes that solidified democracy.

If Chileans decide the constitution should be replaced, they would in October of next year select those who will produce a draft of the new constitution, which will then be put up for a final vote.

Markets across the region reacted positively to the latest developments. Chile’s stocks jumped more than 6% around midday, while the peso gained 3.1% against the dollar. Elsewhere, the Mexican peso and the Colombian peso strengthened against the greenback.

“I think it’s a great step,” said Marta Lagos, a pollster and political analyst. She said a new constitution would serve as the final transition to democracy from the Pinochet years.

But Ms. Lagos said that demonstrators, who have already won concessions from the government in nearly a month of protests, are demanding action to resolve a range of social issues that cannot wait until a new constitution goes into effect.

“Political guarantees are not enough,” she said. “Without social guarantees, there won’t be social peace. There could be a truce but not peace.”

She and other analysts have said the government needs to consider social spending. “That spending needs to be immediate,” she said.

What had started as demonstrations against an increase in subway fares quickly morphed into marches, some of them numbering hundreds of thousands of people. The protesters are angry about low pensions, shoddy schools and inadequate health services. Chileans have also called for changes to an economic system that offers low taxes to corporations and has permitted the privatizations of what had been public services.

Pollster Cadem said Monday in a new poll that 52% of Chileans want to change the constitution, which prohibits public workers from striking and includes strong protections for private property, even allowing for private ownership of water from rivers and other waterways.

***Juan Forero at Juan.Forero@wsj.com