"It is up to the government to assume its responsibilities and persuade... neighbouring countries, particularly Uganda, Rwanda and Burundi, to stop pouring people into Congo," said Cardinal Fridolin Ambongo, who is archbishop of Kinshasa.
Ambongo, speaking at a press conference in the capital, said the Democratic Republic of Congo had to use diplomatic means to get this message across.
The influx, he said, was a source of friction in eastern DRC.
The poor and chronically unstable region is in the grip of militias, some of which are historically rooted in armed campaigns against neighbouring regimes.
The problem does not apply to Congolese of foreign origin who have been in the country for many years -- "no-one can contest their Congolese nationality," the archbishop insisted.
"What is a problem is the influx of others who are arriving and are trying to be passed off as Congolese," he said.
"The most blatant case (is that of) Rwandan immigrants who were forced out of Tanzania some years ago, and ended up being ditched in Congo," he said.
This stirred a "feeling of frustration, of anger... (which) confirms there is a balkanisation plan," he charged.
Ambongo spoke after returning from a pastoral visit last week to the Beni-Butembo region in North Kivu province, where militias have been rampant since the Congo Wars of the 1990s.
The groups include the Allied Democratic Forces (ADF), whose historical roots are Ugandan, as well as the Democratic Forces for the Liberation of Rwanda (FDLR) and a Burundian group, the National Forces of Liberation (FNL).
"The people's situation is dramatic. Because of the lack of security, the people have had to abandon fields, villages, homes, plantations," Ambongo said.
In the last two months, more than 200 civilians have been killed in massacres attributed to the ADF, blamed for more than a thousand deaths since October 2014.
"There has to be nationwide awareness that our country is at war, that the country is in danger," he said, urging the public to support troops who are fighting the militias.
Last month, former DRC prime minister and opposition figure Adolphe Muzito called on the government to "wage war on Rwanda" and even "annex it" to restore peace in the east of the country.
The DRC, a sprawling country the size of continental western Europe, has a history of thorny relations with Rwanda and Uganda.
It has accused those countries of seeking to destablise it, while they allege that the DRC is being used as a rear base by groups seeking to overthrow their governments.