The FDLR are accused of killing hundreds of Congolese this year
Rwanda says two rebel leaders arrested in Germany on Tuesday should be sent home to face trial.
Foreign Minister Rose Museminali told the BBC that she welcomed the arrest of FDLR leader Ignace Murwanashyaka and his deputy Straton Musoni.
However, they have been arrested for war crimes allegedly committed in the Democratic Republic of Congo.
Rwanda accuses some FDLR leaders of having carried out the 1994 genocide against the Tutsi minority.
Mr Murwanashyaka has strongly denied that he or his men have any links to the genocide. He has been in Germany since before the 1994 killings.
Ethnic Hutu, aged 46
Been in Germany since before Rwanda genocide
Denies charges his men are linked to genocide
Says fighting for democracy in Rwanda
Commands 5-6,000 men
FDLR said to smuggle gold from DR Congo to buy weapons
Accused of war crimes and crimes against humanity
Accused of killings, rape, looting and conscripting child soldiers in DR Congo
He says they are fighting to bring democracy to Rwanda, which is now led by a Tutsi-dominated party.
The presence of the largely Hutu FDLR (Democratic Forces for the Liberation of Rwanda) in DR Congo has been at the heart of years of unrest in the region.
Rwanda has twice invaded DR Congo in recent years, saying it had to stop the FDLR from launching attacks on its territory.
UN peacekeepers are currently helping the Congolese army battle the FDLR in an operation which began in January.
Lobby group Human Rights Watch says that in that time, FDLR fighters have killed at least 630 people and raped numerous women. Tens of thousands of people have fled their homes.
"Ignace Murwanashyaka and his colleagues are the ones now fuelling the war that is in eastern Congo," Ms Museminali told the BBC's Focus on Africa programme.
"They are the ones who are collecting money and doing all the political work, canvassing for support. "So we welcome the fact that they've been arrested. We urge that these people are transferred to Rwanda, and they are tried."
Former UN chief investigator in Rwanda Gary Haugen told the BBC that the arrests meant that "a European safe-haven" for the FDLR had been shut down.
"That's very important for trying to bring actual enforcement of international standards against groups which really carry out brutal acts against civilians and war crimes, and crimes against humanity," he said.
One FDLR colonel told the BBC he was saddened by the arrest.
"But perhaps, this will enable Europe to know the truth as they will find out we're not a terrorist organisation," he said.
"But Ignace isn't the only one, we will re-organise ourselves, this isn't an end to our cause."
Analysts say the arrests will be a big blow to the morale of the FDLR fighters and they expect more to surrender in the coming months.
Mr Murwanaskyaka, 46, was arrested in the city of Karlsruhe, while 48-year-old Mr Musoni was held in the Stuttgart area, German prosecutors said in a statement.
"The accused are strongly suspected, as members of the foreign terrorist organisation FDLR, of committing crimes against humanity and war crimes," it said.
It added that "FDLR militias are believed to have killed several hundred civilians, raped numerous women, plundered and burned countless villages, forcing villagers from their homes and recruiting numerous children as soldiers".
The FDLR is accused of funding its arms purchases by smuggling gold and other minerals from areas it controls in the North and South Kivu provinces, just across the border from Rwanda.