State Department spokesman Sean McCormack said Washington "condemns the recent attack by Justice and Equality Movement (JEM) forces ... near Khartoum.
"We call for an immediate end to fighting," he said in a statement, adding that the attacks "undermine the ongoing efforts of the international community to support resolution of the conflicts in Sudan."
The White House, through National Security Council spokesman Gordon Johndroe, said it was "very concerned about the situation" in Sudan," adding that the US Embassy was following developments there "very closely."
"We would urge that both sides cease hostilities, whether it is the rebel group or any response from the government. We want to see calm and order restored," Johndroe added in his statement.
McCormack said the United States "implores both JEM and the Government of Sudan to guard against attacks against civilians in Omdurman and Darfur, and warns both sides against taking any retaliatory action based on ethnicity or tribe."
The US statements were issued as Sudanese authorities said that the army had repulsed an unprecedented attack on the capital Khartoum by Darfur rebels, following heavy clashes and the imposition of an emergency curfew.
"The operation is a failure," senior National Congress Party member Kamal Obeid told AFP after troops clashed with Islamist rebels across the river from Khartoum in its twin city of Omdurman, where witnesses had reported heavy fighting.