Sudan and Chad repeatedly have accused one another of backing rebels in each other's countries, and both have denied the allegations. Both countries also have signed peace deals promising to stop the border fighting.
U.S. Deputy Secretary of State John Negroponte also repeated a demand he made a day earlier that Sudan stops its support of the janjaweed militia blamed for atrocities in Darfur.
Sudan's government has always denied backing the janjaweed, despite accusations that it does so from the United Nations, the African Union and the International Criminal Court.
"There is widespread agreement that the crisis in Darfur has three main elements, humanitarian, security and political. All of these elements demand the immediate attention of the Sudanese government and international community," Negroponte told journalists after visiting a camp for Sudanese refugees in eastern Chad.
He said he welcomed Sudan's decision announced a day earlier to allow the U.N. to send 3,000 peacekeepers to Darfur, but did not comment further on the issue.
Sudan and Chad should, "cease supporting any armed elements, rebel or ethnic militias that seek to destabilize the neighbor," said Negroponte. "Sudan must cease its support of the janjaweed and all non-signatories of the Darfur peace agreement must stop their attacks, put down their arms and come to the negotiating table."
The U.S. diplomat also said that the United States is convinced that the violence in Sudan's western region of Darfur, Central African Republic and Chad are linked and their stability depends on each other.
On Monday, Negroponte met with President Idriss Deby and Foreign Affairs Minister Ahmat Allam-mi. Later Tuesday, Negroponte was to go to Libya and then visit Mauritania.