Rwanda, running unopposed for the seat being vacated by South Africa, received 148 of the General Assembly's 193 votes. It needed two-thirds of the total, or 128, to be elected.
Other countries elected for 2013 and 2014 were Argentina, which also ran unopposed, getting 182 votes; Australia and Luxembourg, defeating Finland to take the two seats in the "Western European and Others" category; and South Korea, which beat Cambodia and Bhutan for the Asia-Pacific seat.
The delegation from the Democratic Republic of the Congo, a large central African country formerly named Zaire, spoke against Rwanda's bid before the secret ballot.
Its members accused the government of Prime Minister Pierre Habumuremyi of hosting "war criminals operating in the eastern part of the DRC who are being sought by international justice."
A June report by a U.N. experts panel accused senior Rwandan security officials, including Defense Minister Gen. James Kabarebe, of funding and supplying arms to the rebel military March 23 Movement in its six-month anti-government insurgency that has driven more than 260,000 people in the eastern North Kivu province to flee since April.
That part of Congo has faced internal fighting since 2003.
A final confidential U.N. report from the experts, delivered to the body's sanctions committee Friday and then leaked to the news media, said Rwanda's M23 support continued.
Rwandan Foreign Minister Louise Mushikiwabo attacked the report, accusing its writers of having a political agenda that led to "incendiary anti-Rwanda writings."
"Rwanda will not allow itself to be dragged any deeper into this farce by responding to the group's far-fetched but fact-free assertions," The Wall Street Journal quoted her as saying.
Congolese President Joseph Kabila told the General Assembly's annual meeting in September the U.N. Security Council should impose sanctions against those providing "external support" to Congo's rebels, without mentioning Rwanda by name.
"We expect the community of nations will shoulder its responsibility, and the Security Council will ensure compliance," he said.
But diplomats Thursday told the Journal that might be difficult now that Rwanda can argue its case inside the 15-member Security Council.
Rwanda would not have veto power. The council's five veto-holding permanent members are the United States, Britain, France, Russia and China.