Bosnian media said on Friday the survey by the United Nations Development Programme covered 1,650 people.
In the Croat-Muslim Federation, 50.3 per cent of those polled said they supported the draft changes while 4.5 per cent were against them. In the Bosnian Serb entity, only 26.9 per cent were in favour.
The changes were supported by 51 per cent of Bosniaks, 48 per cent of Croats, and only 26.9 per cent of Serbs.
The state parliament's House of Representatives is expected to vote on amendments to the Constitution on April 25. State Presidency chairman Sulejman Tihic said earlier this week that 27 of the 42 deputies would support the changes, which is the qualified majority.
The front pages of nearly all influential dailies today carried a warning conveyed on behalf of the Unites States administration by Rosemary Di Carlo, a State Department official in charge of Eurasia.
She was quoted as saying that the constitutional changes were the first step to a more effective government which would function in accordance with European standards and carry out the necessary reforms in the coming years so that Bosnia and Herzegovina could become a full member of the European Union and NATO.
If you do not pass the first, you will never get to the next stage of the changes, Di Carlo was quoted as saying.
She indirectly indicated that without the adoption of constitutional amendments, one could not expect the closing of the Office of the High Representative envisaged for the first half of 2007.