What you need to know:
- DR Congo Foreign Minister Christophe Lutundula last week vowed his country would "safeguard its territorial integrity," in a statement that Rwanda said was a threat.
- Qatar's efforts to organise the meeting started during the football World Cup, which it hosted. Kagame was present at the final on December 18.
Qatar is battling to host a peace meeting between the presidents of rivals DR Congo and Rwanda, even though a summit this week was called off amid rising tensions, diplomats say.
With a rebellion in eastern DR Congo already complicating relations, Rwandan forces this week opened fire at a Congolese fighter jet that they said had violated Rwandan airspace.
Qatar had planned a meeting of Rwanda's Paul Kagame and DR Congo's Felix Tshisekedi on Monday and a deal to ease tensions was ready, but Tshisekedi refused to attend, diplomats said.
"The intended signing meeting between the presidents of Rwanda and DR Congo has been postponed until further notice," a Qatar foreign ministry source told AFP.
"Qatar is optimistic that the meeting will take place at a time to be determined."
The source said DR Congo had requested "facilitation" in an "official letter" and "both parties agreed to initiate it in Doha."
Qatar's efforts to organise the meeting started during the football World Cup, which it hosted. Kagame was present at the final on December 18.
One "high-level" meeting between DR Congo and Rwandan officials was held during the tournament, according to a source with knowledge of the talks.
An African diplomat following the peace efforts said however that Tshisekedi had refused to attend the Doha signing ceremony this week because of "doubts" about the accord. The diplomat gave no details.
Relations between the giant Democratic Republic of Congo and its far smaller neighbour have been poor for decades.
But they flared sharply last year after a long-dormant rebel group, the M23, revived operations in DR Congo's troubled east and captured swathes of territory.
The Kinshasa government accuses Rwanda of supporting the rebels.
Rwanda denies this and in turn accuses DR Congo of abandoning a truce agreement forged in the Angolan capital Luanda and Nairobi, Kenya's capital.
Renewed fighting between the DRC's armed forces and the M23 has stoked tensions, sharpening concern in western capitals.
DR Congo Foreign Minister Christophe Lutundula last week vowed his country would "safeguard its territorial integrity," in a statement that Rwanda said was a threat.
The latest fighter jet incident has only heightened concerns. DR Congo called it "an act of war."
Diplomats said the United States was backing the effort to mediate by Qatar, which has played go-between in several conflicts in recent years.
Qatar wants "concrete results," the foreign ministry source said, without giving details.
"As a facilitator of the agreement, Qatar will spare no efforts" to help Rwanda and DR Congo achieve "stability and prosperity," the source said.
Rwandan government spokesperson Yolande Makolo, in a text message to AFP, said "Rwanda is always ready to contribute to peace and security in our region.
"We look forward to the meeting in Doha in order to reinforce the Nairobi and Luanda processes."
Scores of armed groups roam the east of the mineral-rich DRC, many of them a legacy of two regional wars at the end of the 20th century that claimed millions of lives.