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Gunfire erupted in several areas in the capital Kinshasa, as Congo's long-serving president, Joseph Kabila appeared set to stay on despite the expiration of his mandate.

Shots rang out early on Tuesday in several parts of the sprawling city of 10 million, particularly in two northern quarters after whistles - an opposition sign of protest - were heard.

Demonstrators also beat on improvised drums, demanding the 45-year-old Kabila, who has led the Democratic Republic of Congo since 2001, to quit the top job.

Kabila's second term officially expired on Tuesday.

Opposition leader Etienne Tshisekedi called on the Congolese people to peacefully resist Kabila.

"I launch a solemn appeal to the Congolese people to not recognise the ... illegal and illegitimate authority of Joseph Kabila and to peacefully resist [his] coup d'etat," Tshisekedi said in a video posted on YouTube.

The declaration appeared to be an effort by Tshisekedi and opposition leaders to reinject themselves into the drama surrounding the conclusion of Kabila's mandate, after they originally declined to call for mass protests.

A muffled explosion was also heard in the posh quarter of Gombe, where the presidential palace is located. Residents said tear gas shells were fired in other areas.

Talks on a peaceful transition are in limbo, sparking fears of new violence in the unstable, mineral-rich nation.

Kabila, who has been in power for 15 years, is constitutionally barred from seeking a third term, but under a recent constitutional court order, he may stay on until a successor is chosen.

The ruling party and some opposition leaders have agreed to schedule an election in April 2018, at the earliest, leaving Kabila in office until the vote. But the main opposition bloc rejects this plan.

Security was also tight in the second city, Lubumbashi, in the southeast.

Social networks have been cut or filtered since midnight Sunday, on government orders, and police at the weekend banned gatherings of more than 10 people.

'Kabila won't cave in'

In a last-ditch bid to achieve a peaceful transfer of power, the ruling party and opposition groups held talks last week with the mainstream opposition led by Tshisekedi.

But after a week of mediation, they were suspended and due to resume on Wednesday.

"I don't see [Kabila] caving in to pressure," his diplomatic adviser Barnabe Kikaya Bin Karubi said Monday.

A democratic handover would break new ground for Congo's 70 million people who, since independence from Belgium in 1960, have never witnessed a democratic transfer of power following elections.

The president has been in office since his father, Laurent Kabila, was assassinated in 2001. He was elected in 2006, and again in 2011, in a poll the opposition decried as rigged.

Some two decades ago, Congo sank into the deadliest conflict in modern African history, its two wars in the late 1990s and early 2000s dragging in at least six African armies and leaving more than three million dead.