A team of UN Security Council ambassadors has called on Rwanda not to invade the neighbouring DR Congo to hunt down Rwandan Hutu rebels there.
Some 10,000 UN peacekeepers are already in eastern DR Congo
Rwandan President Paul Kagame renewed a threat to attack "when the time was right", indicating it could be soon.
Hutus were attacking Rwandan villages from camps in eastern DR Congo, under the noses of the international community, he said.
The UN said it "strongly exhorts" Rwanda not to breach international law.
The ambassadors said any invasion could threaten regional stability and DR Congo's peace process.
"There are clear bases known to us of these ex-FAR/Interahamwe (rebels). At the appropriate moment we will certainly take measures about that," Mr Kagame said.
Regional analysts say Rwanda could be exaggerating the threat to try and maintain control of parts of eastern Congo.
Rwanda has twice invaded its western neighbour over the past decade and although it withdrew its troops in 2002, deep distrust remains between the two countries.
Some of Rwanda's Hutu rebels who took part in the 1994 Tutsi genocide fled across the border to eastern DR Congo.
Chief UN spokesman Fred Eckhard said a deployment of an extra 5,900 troops - agreed last month - had begun.
There are already more than 10,000 UN peacekeepers in DR Congo and troops have been placed on alert and patrols have been despatched to check for any Rwandan incursion.
Mr Eckhard said the deployment would bring additional security to the border area following Rwandan threats.
"The mission's mandate includes preventing the DRC peace process from being derailed by spoilers from within and outside the DRC," he said from the UN's New York offices.
The crisis comes as representatives of the UN Security Council complete a tour of the region to strengthen security measures.
A Rwandan representative told Reuters news agency that Hutu rebels were advancing towards the country and that Rwanda would be ready to see them off.
"There are a number of operations and mass movements of rebels towards our border," said Richard Sezibera, adviser to President Paul Kagame.
"We shall take whatever means it takes to protect our borders. Our response to provocation is that nothing is ruled in and nothing is ruled out."