The State Department is commending Khartoum authorities and southern leaders for their appeals for calm following Mr. Garang's death.
But officials here are making clear they believe more can be done to control the violence, which threatens a new north-south split in the country only a month after a national unity government took office.
More than 100 people have been reported killed in three days of rioting in the capital, Khartoum, and the key southern city of Juba, which followed the death in a helicopter crash of Mr. Garang, the longtime southern rebel leader who became first vice president of the unity government.
News accounts say the unrest has included clashes between northern Arabs and southern Sudanese, who believe Mr. Garang's death was not an accident despite official accounts that the crash was due to bad weather.
At a news briefing, acting State Department Spokesman Thomas Casey said the United States is deeply concerned about the violence and he echoed calls by the unity government and the southern rebel movement (SPLM) for calm and restraint.
He acknowledged government moves to boost the security presence in trouble spots but said more needs to be done.
"It's our understanding that the government has deployed additional security forces to Khartoum and other areas to stop the violence," said Mr. Casey. "And the United States joins the rest of the international community in calling for the government to urgently take the additional steps that may be necessary to send a clear message to all the people of Sudan regarding its determination to halt the violence."
Mr. Casey said the United States remains committed to the cause of peace in all of Sudan including implementation of the North-South peace accord and a resolution of the crisis in Darfur.
He said it urges all Sudanese to work to achieve the vision the late Mr. Garang had for a united, prosperous and peaceful Sudan.
Secretary of State Condoleezza Rice sent two senior officials, Assistant Secretary of State for African Affairs Constance Newman and special envoy for Sudan Roger Winter, to Sudan after the death of Mr. Garang was confirmed early this week.
In southern Sudan Wednesday, they paid a condolence call on Mr. Garang's widow and met with his successor as SPLM leader, Salva Kiir Mayardit, who will also succeed him as the country's first vice president.
Under questioning here, spokesman Casey said the United States has no reason to believe that the helicopter crash in Uganda that killed Mr. Garang and several others last Saturday was anything other than accidental.
Ugandan President Yoweri Museveni has set up a panel of experts to investigate the crash of the Russian-made helicopter.
Mr. Casey said that at the request of the Ugandan leader and Mr. Salva Kiir, the United States is sending experts from the U.S. National Transportation Safety Board to assist in the inquiry.
That federal agency investigates U.S. domestic civil aviation accidents.