Left-wing candidate Michelle Bachelet has won the first round of voting in Chile’s presidential election.

But with most of the votes counted, Ms Bachelet has conceded that she has failed to reach an outright majority and avoid a run-off.

She took nearly 47% of the vote. Her main rival, Evelyn Matthei, who was a minister in the centre-right government of Sebastian Pinera, got 25%.

A second round of voting will take place on 15 December.

“Reaching the second is undoubtedly a great triumph,” Ms Matthei posted on her Twitter account.

“When this project began, many doubted we would be here. But here we are,” she wrote.

She told supporters in Santiago: “The country has mostly voted for the proposal that we have made for Chile, so that Chile will be once and for all the modern and fair country that we want.”

“We won tonight and we will work to win by an ample margin in December.”

Most opinion polls had indicated a victory for Ms Bachelet in the first round.

A paediatrician by training, Ms Bachelet was Chile’s first woman president between 2006 and 2010.

She was constitutionally barred from serving a second successive term and was very popular when she left office.

Sunday’s vote went ahead without major incidents.

But students, who for years have been staging protests demanding educational reform, occupied Ms Bachelet’s campaign headquarters.

They laid out a banner outside the building which read: “Change is in the streets, not in the Moneda [Presidential Palace].”

Ms Matthei entered the race after two candidates of the centre-right alliance resigned, earlier this year: one for alleged financial irregularities, the other one after struggling with depression.

Evelyn Matthei, 60, has called for a continuation of the policies of outgoing President Sebastian Pinera, asserting that Chileans are “better off” now than when he came to power four years ago.

Speaking after it became clear a second round would take place, she wrote on Twitter: “Let us fight for the votes of the other seven candidates now, and for those of Michelle Bachelet.”

Ms Bachelet leads an alliance of her Socialist Party, Christian Democrats and Communists and has campaigned on policies designed to reduce the gap between rich and poor.

Chile is one of the richest countries in Latin America, but millions have staged protests over the past few years to push for a wider distribution of wealth and better education.

Ms Bachelet, 62, wants to increase taxes to offer free university education and reform political and economic structures dating from the dictatorship of Augusto Pinochet, who ruled from 1973 to 1990.

Her manifesto this time is much more radical than before, says the BBC’s Gideon Long in Santiago.

Ms Bachelet and Ms Matthei are the daughters of air force generals, once friends, who found themselves on opposite sides of the political divide once Gen Pinochet came to power.

As children in the 1950s, they were neighbours and used to play together on the airbase where their fathers worked.

Under Gen Pinochet, Evelyn Matthei’s father, Fernando, rose up the ranks to run a military school.

Michelle Bachelet’s father, Alberto, who worked for the Socialist administration overthrown by General Pinochet, died of a heart attack in 1974.

An investigation concluded that the 51-year-old general probably died of heart problems aggravated by torture sessions at the military academy.

A judge ruled earlier this year that General Matthei had no knowledge or involvement in the torture.

The lower house of congress and half the senate are also being elected.