Rwanda will retaliate if it suffers further attacks from neighbouring Democratic Republic of Congo, its foreign minister said on Tuesday, after accusing Congo of firing shells across the border earlier this month.

Congo summoned Rwanda's ambassador and suspended RwandAir flights to Congo over the weekend in response to what it said was Kigali's support for M23 rebels carrying out a military offensive in its eastern borderlands.

Rwanda denies the claims and has in turn accused Congo's army of fighting alongside the Democratic Forces for the Liberation of Rwanda (FDLR), an armed group founded by ethnic Hutus who fled Rwanda after participating in the 1994 genocide.

"If attacks continue we will not sit idly by... Rwanda will have the right to respond to protect the security of the country, to protect the security of its citizens and we have the means to do that," Foreign Minister Vincent Biruta told reporters.

Biruta said FDLR fighters were among the ranks of Congo's army when their shells allegedly destroyed houses and injured people on the Rwandan side of the border.

"They cannot say that they are victims of the FDLR. The FDLR are killing our people, not the Rwandan people; it is we who suffer. Their discourse on the FDLR no longer makes sense," Congo government spokesman Patrick Muyaya told Reuters.

The clashes threaten to unravel relations between the two countries, which had improved since Congolese President Felix Tshisekedi came to power three years ago.

The M23 insurgency stems from the long fallout from the 1994 genocide in Rwanda.