Rwandan soldiers shot dead a Congolese soldier who crossed the border and shot at security forces on Friday, triggering a brief exchange of fire between the two sides, Rwanda's defence ministry said.
Already strained relations between the central African neighbours have deteriorated sharply since the M23 rebel group launched a fresh offensive in eastern Congo in March last year, displacing over 600,000 people since.
Congo accuses Rwanda of backing the Tutsi-led group. The United Nations, the United States, France and other international powers have made similar allegations.
But Rwanda denies this and says it is being scapegoated for Congo's military incompetence.
The incident at the border took place on Friday evening when the Congolese soldier crossed into western Rwanda from the Grande Barriere border post, outside the city of Goma, and shot at Rwanda Defence Force (RDF) soldiers, the ministry said.
"The RDF soldiers returned fire, killing the FARDC soldier on the Rwandan side of the border. Several other FARDC soldiers fired at the RDF position resulting in a brief exchange of fire," it said in a statement.
"The situation is now calm," it added, noting that many similar incidents have occurred in the past.
Colonel Guillaume Ndjike, a spokesperson for Congo's army in North Kivu province, said he could not yet comment on the incident but would do so on Saturday.
Rwandan armed forces shot and killed a Congolese soldier in very similar circumstances last June.
The M23, which is waging its most sustained offensive since capturing swathes of territory in 2012-13, has been accused of flouting a ceasefire process and summarily executing civilians.
The unrest has spurred anti-Rwandan sentiment in Congo and local opposition to a UN peacekeeping mission.
A fresh exodus of people fled towards Goma from the nearby town of Sake last week as the M23 appeared to gain more ground, bringing the rebels closer to the key trade hub.