Uganda's president is denying support for rebels opposed to Rwanda's government as tensions between the two East African neighbors persist, raising fears of a possible armed conflict.

In a letter to Rwandan President Paul Kagame published on Tuesday in government-controlled media, Ugandan President Yoweri Museveni said that "there is no question of Uganda supporting anti-Rwanda elements."

Both presidents have recently made remarks seen as threatening to each other, with the Ugandan leader warning that "those who try to destabilize our country do not know our capacity" and Rwanda's president countering that "nobody anywhere can bring me to my knees."

Rwanda's government has closed a busy border crossing with Uganda, and Rwanda's government has ordered its citizens not to travel to Uganda.

An official with the Ugandan presidency confirmed Museveni authored the private letter to Kagame in effort to assuage the Rwandan leader's concerns. Uganda has been accused of extending help to the Rwanda National Congress, an opposition group in exile that is led by former Rwandan army chief Kayumba Nyamwasa.

Nyamwasa, who lives in South Africa, has survived at least two assassination attempts he believes were ordered by Rwandan authorities. Rwanda, which denies targeting Nyamwasa, has outlawed his group and accuses it of operating rebel cells in eastern Congo.

In the letter published in the Ugandan newspaper The New Vision, Museveni acknowledged he recently met with a member of the Rwanda National Congress who spoke of "bad things" happening in Rwanda and who "wanted us to support them."

Museveni also met separately with an exiled Rwandan tycoon, Tribert Rujugiro, who is accused by Rwandan authorities of financing rebels opposed to Kagame, according to Museveni's letter to Kagame. Rujugiro's business in Uganda, notably a big tobacco processing plant, is one of the contentious issues, with Kagame demanding that Rujugiro divests out of Uganda.

It appeared Museveni would not move to forcibly shut down or sell Rujugiro's business.

"If, therefore, he is still a problem to Rwanda, the correct option is to use the courts of Uganda to prove the case of terrorism and then his assets can be frozen," Museveni wrote to Kagame on March 10, talking about Rujugiro.

Rujugiro himself denies supporting anti-Kagame groups.

"Kagame knows that if I opted to help the rebels fighting against him, it would take less than six months to defeat him," he said in an interview with the New Vision.

Tensions between Rwanda and Uganda, as well as between Rwanda and Burundi, "are reaching an alarming level" and "could lead to another proxy conflict in eastern [Congo]," according to analysis by the South Africa-based think tank Institute for Security Studies.

In recent years Rwanda also has sparred with Burundi over charges Burundian rebels are based across the border in Rwanda.

In the 1990s, the armies of Uganda and Rwanda went to war in eastern Congo where they backed rival rebel groups. Much of eastern Congo remain lawless, with many armed groups still operating there.

Kagame and Museveni, strong leaders who have ruled their countries for many years, have increasingly disagreed in recent years as Kagame, once an intelligence lieutenant for Museveni, asserts his authority at home and in the region.

Kagame, who grew up as a refugee in Uganda, was a Ugandan army major before he led the Uganda-backed rebels who took power in Rwanda at the end of the 1994 genocide.

VOA