Burns said this at a news conference held after his meeting with top Bosnia-Herzegovina officials.
The US official said the time had come for Bosnia to elect one president, one prime minister with strong powers and an efficient parliament as was the case in democratic European countries.
The clear incentive from Washington for radical changes of the Dayton Constitution arrived in Sarajevo ahead of the marking of the tenth anniversary of the signing of the document.
Burns said the US Administration would on that occasion, on 21 November, organise a special ceremony at which Bosnian senior officials would be invited. He said he would use this opportunity to talk to US State Secretary Condoleezza Rice and Congress leaders.
Answering a reporter's question if the United States expected the announced changes to result in the cancellation of the Bosnian Serb entity, Burns said this decision was up to Bosnian citizens and their political leaders.
He, however, stressed that the establishment of a third entity in Bosnia was unacceptable for the United States. The establishment of the third entity has been proposed by representatives of the Croatian Democratic Union of Bosnia-Herzegovina.