French President Emmanuel Macron met Wednesday with the leaders of Rwanda and the Democratic Republic of Congo, seeing progress in easing tensions that have flared in recent months.

On the sidelines of the United Nations General Assembly, Macron invited Rwandan President Paul Kagame to lunch with his DR Congo counterpart Felix Tshisekedi, who a day earlier had accused Kigali of backing rebel attacks in his country.

The three leaders together "noted their concerns about the resurgence of violence in the east of the DRC," the French presidency said in a statement.

France said that Kagame and Tshisekedi agreed on the need for the pullout of M23 rebels from the strategic town of Bunagana on the Ugandan border.

The three leaders want to "intensify lasting cooperation to fight impunity and put an end to activities of armed groups in the Great Lakes region," including the Democratic Forces for the Liberation of Rwanda, or FDLR, the statement said.

Kagame's government has demanded a crackdown on the FDLR, a Rwandan Hutu group that Kigali views as a threat due to links to the 1994 genocide.

But the M23, a separate, mostly Tutsi group in the violence-wracked east of DR Congo, has been the focus of recent tensions. 

In his address to the General Assembly on Tuesday, Tshisekedi alleged that Rwanda has provided "massive support" to M23, which he blamed for the shooting down of a UN peacekeeping helicopter in March, in which eight people died.

"Rwanda's involvement and responsibility is no longer debatable," he said.

Kagame called for calm in his own address on Wednesday.

"There is an urgent need to find a political need to find and address the root cause of instability in eastern DRC," Kagame said.

"The blame game does not solve the problems. These challenges are not insurmountable and solutions can be found," he said.

"This would ultimately be much less costly in terms of both money and human lives."

Kagame's government has long rejected allegations of backing the M23, but US Secretary of State Antony Blinken, on an August visit to Kinshasa, said there were "credible" reports of Rwandan support.