Abdalla Hamdok’s convoy was attacked with explosives and gunfire on Monday.
It is not yet clear who was behind the attack and the arrival of the three US investigators follows a call from the Sudanese authorities for foreign assistance.
Mr Hamdok, an economist, was appointed to head the transitional government following the overthrow last April of the long-standing President, Omar al-Bashir.
Correspondents say there are concerns over Sudan’s stability given some once powerful personalities are opposed to the widespread political and security reforms taking place.
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