In Kigali, the government said it "regrets the unilateral closure of the border by Burundi".
Burundi closed its border with Rwanda in 2015 amid mutual claims of supporting rebel groups.
Burundi said on Thursday it had closed the border with Rwanda, nearly two weeks after accusing its neighbour of supporting rebels who carried out attacks on its soil.
Burundi says the RED-Tabara group staged an attack on December 22 near the border with the Democratic Republic of Congo (DRC), killing 20 people, including women and children.
President Evariste Ndayishimiye has since accused Rwanda of backing the rebels -- a claim denied by the Rwandan government.
In Kigali, the government said it "regrets the unilateral closure of the border by Burundi".
"This unfortunate decision will restrict the free circulation of people and goods between the two countries and violate the principles of regional cooperation and the integration of the East Africa Community," a statement said.
The RED-Tabara group, which has a base in the eastern DRC province of South Kivu, emerged in 2011 and is now the most active of Burundi's rebel forces with an estimated 500 to 800 fighters.
"We have closed our borders (with Rwanda), anyone who tries to go there will not get through. The decision has been made," Burundi's Interior Minister Martin Niteretse told reporters on Thursday.
"After having noted that we had a bad neighbour, (Rwandan President) Paul Kagame... we stopped all relations with him until he returns to better feelings," the minister added.
He said Rwanda "shelters criminals who harm Burundians".
"Rwandan nationals, we don't want them," Niteretse said.
A witness present at the Kanyaru-Haut border post told AFP they had crossed the border at around 1240 GMT and that it had been closed shortly afterwards.
Relations between Burundi and Rwanda have often been tempestuous.Â
Although ties began improving after Ndayishimiye took power in 2020, they have soured again over Burundi's involvement in the DRC.
Burundian forces have for several years been conducting joint operations with their Congolese counterparts against rebels in the restive and mineral-rich eastern DRC, which has long been plagued by numerous armed groups.
One of them, the M23 rebellion is supported by Rwanda, according to Western governments and the United Nations -- allegations Kigali denies.Â
Burundi closed its border with Rwanda in 2015 amid mutual claims of supporting rebel groups. The border was reopened in 2022.
RED-Tabara is accused of waging deadly violence in the East African country since 2015 but had not been active there since September 2021, when it carried out several attacks, including on the airport in the main city of Bujumbura.
"These armed groups have been provided with shelter, food, offices and money from the country that hosts them. I mean Rwanda," Ndayishimiye said at the end of last month.
In Kigali, the government denied the claims, saying in a statement sent to AFP at the time: "Rwanda is not associated, in any way, with any Burundian armed group."
RED-Tabara claimed responsibility for the attack in a message on X, formerly Twitter, saying it targeted a border post and killed nine military personnel and a policeman.
In another post on X, it denied killing any civilians and said the group "is not supported by any country. It only has the support of the Burundian people".
Burundi also joined an East African force that was deployed in November 2022 to quell the DRC violence but its soldiers withdrew last month after Kinshasa refused to extend the mission's mandate.
