If the 2014 general election is held under the existing Constitution, we will have a problem recognising its results, she told reporters in Banja Luka.
She recalled that the leaders of all major political parties had committed to proposing solutions that would remove from the Constitution and the electoral law provisions which prevent national minorities from running for the state Presidency and the state parliament's upper house.
During negotiations with European Commission representatives in July, they committed to jointly proposing by August 31 a way to implement a European Court of Human Rights ruling which found that the Bosnian Constitution and electoral law discriminate against national minorities.
Hennessey said the deadline was just days away but that no agreed solution was in sight.
The political crisis in the country following the break-up of the ruling coalition has brought negotiations on a joint proposal to a standstill and it is uncertain when they will resume.
It is disappointing that again nothing has been done, Hennessey said, adding that Bosnia would punish itself if it held elections under existing rules, as its Stabilisation and Association Agreement with the European Union could not go into force.
She said that before possible accession to the EU, Bosnia must ensure genuine and stable democracy and function as a state, which she said was not the case now.