Figures released by the European Security Organisation (OSCE) show the Muslim-based Party for Democratic Action (SDA) has taken 26.8% of the vote.
Although multi-ethnic parties did well in Bosnia's Muslim-Croat federation, a nationalist party seems set to capture the presidency of the Serbian half of Bosnia-Hercegovina.
"Regrettably, this has not yet been fully achieved", he said.
With 86% of votes counted, Muslim nationalists were running neck and neck with the multi-ethnic opposition Socal Democratic Party (SDP).
Figures released by the European Security Organisation (OSCE) show the Muslim-based Party for Democratic Action (SDA) has taken 26.8% of the vote.
That puts it slightly ahead of the more moderate SDP with 26.3%.
The hardline Croatian Democratic Union - which was leading on Monday - came third with 17.6%.
The International Crisis Group, a think tank, called the SDP showing "the only encouraging thing about this election."
Nationalists lead
In the Serb republic - which forms the other half of Bosnia-Hercegovina - the nationalist Serb Democratic Party (SDS) retained its lead.
Led by incumbent Vice-President Mirko Sarovic, the SDS was founded by Radovan Karadzic, Bosnia's most prominent figure to be indicted for war crimes.
The International Crisis Group (ICG) described the SDS as "a party designed to commit war crimes."
The SDS says it has changed since its ultra-nationalist days and that it has nothing to do with Mr Karadzic.
But the ICG says Mr Karadzic still controls the SDS from behind the scenes.
Pragmatist weakened
The strong SDS showing looks likely to defeat Prime Minister Milorad Dodik's bid for the presidency.
His pragmatic, pro-Western forces in the government have had to shoulder the burden for the Bosnian Serb republic's economic ills.
But he may still be able to form another government with his traditional support of non-nationalist Serbs as well as Muslims and Croats.
He can only do that if he secures the backing of a new middle-of-the-road party, headed by the prominent economist, Mladen Ivanic.
Results coming in
It will take several more days before full, official results are published and talks begin, to form new governing alliances in the Bosnia-Hercegovina House of Representatives.
The partial re-integration of Bosnia - as envisaged at the 1995 Dayton peace talks - has now been going on for five years.
International forces have the power to ban parties or individuals they consider to be counter-productive.
The US deputy ambassador to the UN, James Cunningham, said the US favoured that course of action.
"We will continue to urge that obstructionists are kept out of government", he told the UN on Tuesday.
The Saturday polls are the third since the signing of the Dayton Agreement, which ended three years of inter-ethnic strife.