The U.S. initiative follows a renewed outbreak of violence in east Congo and a pledge by President Joseph Kabila last week to begin forcibly disarming rebel fighters loyal to former army general Laurent Nkunda.
Kabila is to meet U.S. President George W. Bush at the White House Friday and is expected to discuss security issues.
Government and rebel forces have been accused of drastic human rights violations including mass rape, as the government has struggled with little success to establish authority over the lawless eastern regions of the country, which are thousands of miles from Kinshasa, the capital.
Frazer said in testimony at a Senate Foreign Relations Committee hearing that the U.S. military training would be aimed at improving the national army's discipline and enforcement of human rights.
The United States has already been involved in training at an officer level, but is expanding those efforts.
"We are now considering direct military training of a limited number of army units so that they can have the capacity to deal with the negative forces," Frazer told the subcommittee on African affairs. In an interview following her testimony, Frazer would not detail what the training would entail.
Nkunda left the army and formed his own militia soon after Congo's war ended in 2002, claiming he needed to protect his minority Tutsi ethnic group from Rwandan Hutu rebels who took refuge in eastern Congo following Rwanda's 1994 genocide.
Congo's government has struggled with little success to establish authority over the lawless eastern regions of the country, which are thousands of miles from Kinshasa, the capital.
Since January, between 400,000 and 500,000 people have been displaced by fighting in Congo's North Kivu province, according to the United Nations.
When pressed by subcommittee chairman, Sen. Russ Feingold, a Democrat, Frazer said that the United States is prioritizing diplomatic efforts to end the conflict.
"The United States and other donors must send a strong signal that a more militarized policy is simply not acceptable," Feingold said.
On Wednesday, Nkunda's rebels said they would send 200 of their fighters to rejoin the country's national army as part of negotiations to end violence in the region, potentially a major step toward ending a resurgence of violence.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
The TurkStream, which runs along the bottom of the Black Sea from Russia's Anapa to Turkey, will consist of two lines, each with a capacity of 15.75 billion cubic meters of gas a year