A UN Security Council meeting about the deadly clashes, originally set for Monday, has been moved to Sunday due to the escalating conflict.
The M23 group has called on Congolese troops in Goma to surrender in order to avoid bloodshed. While DR Congo has severed diplomatic ties with neighbouring Rwanda, accusing the country of being behind the rebellion.
The move comes after M23 fighters killed a Congolese military governor who was visiting the frontline on Thursday. Earlier in January, they captured the key eastern Congolese towns of Minova and Masisi.
Macron called for an end to the fighting in separate calls with the leaders of DR Congo and Rwanda on Saturday, his office said.
The EU’s foreign policy chief Kaja Kallas urged the M23 to halt its advance and condemned Rwanda’s support for the group, the AFP news agency reports.
Further condemnation came from Angolan President Joao Lourenco, the African Union’s mediator between Rwanda and DR Congo, who denounced “irresponsible actions by the M23 and its supporters” and called for the “immediate cessation” of fighting to preserve civilian lives, according to the AFP news agency.
Fighting between the M23 and DR Congo’s army has intensified since the start of the year, with the rebels seizing control of more territory than ever.
The conflict has already led more than 400,000 people to flee their homes this year, according to the UN.
Local leaders last week said more than 200 civilians had been killed in areas captured by the M23, with hospitals in Goma treating hundreds of patients.
Martin Gordon, an Anglican bishop in Goma, told the BBC fighting in the country had gone on “way too long” and people “will do anything for peace”.
In the past few days, several countries have urged their citizens to leave Goma, including the UK, France, Germany and the US.