In an unusual election report, Mr van Thijn praised the technical operations on polling day but denounced the hostile political climate in which the vote was held.
"In my opinion the elections were technically well prepared and carried out successfully under difficult circumstances," he said. "However, the general climate in which the elections took place was in some places below the minimum commitments" required by the organisers, the Organisation for Security and Co-operation in Europe (OSCE).
The monitors' report included examples of electoral irregularities, such as "family voting" - one person casting several ballots on behalf of the household - and some intimidation of voters.
But the biggest problems, affecting thousands of voters, were errors in the electoral register, which meant that many people were not allowed to vote.
Most concern was expressed at the restrictions on freedom of the media, of movement and of expression in the run-up to the election, and Serb campaigning against the desire expressed in the Dayton agreement for a united Bosnia.
As a result, Mr van Thijn set as his condition for validating the elections a request that the ruling Serb party should agree in writing to change its constitution and the platform of independence from Bosnia.
This sits somewhat at odds with early statements from the Serb-held half of the country, where the leadership openly campaigned for partition: "First signs are that the Serbs overwhelmingly voted for Republika Srpska," Velibor Ostojic, deputy premier, said on Sunday.
Mr van Thijn is therefore asking the party to renounce the single issue on which it won the election.
The request was seen by some observers as the strongest critical statement Mr van Thijn felt able to make, given that the West is unwilling to see the Dayton peace process falter three months before Nato's peace force is scheduled to leave Bosnia.
With results for the three-man presidency in from 22 of the 109 municipalities, the three nationalist leaders were well ahead - as expected. Alija Izetbegovic of the SDA had won 82 per cent of the Muslim vote, Momcilo Krajisnik (SDS) 85 per cent of the Serb vote, and Kresimir Zubak (HDZ) 90 per cent of the Croat vote.
As one observer noted, the elections were seen by many as a continuation of the war by other means, the climate exploited by the three ruling nationalist parties.
The International Crisis Group, whose monitors worked under Mr van Thijn, issued a statement arguing that against a background of "adverse conditions, electoral engineering and disenfranchisement, these elections cannot be described as free, fair or democratic".
To some extent, Mr van Thijn agreed when asked to comment on the statement. "I didn't say that they were free and fair," he said.
One Western diplomat commented: "That was a man under tremendous pressure."
Mr van Thijn denied this interpretation. "Before certifying the elections we knew that the conditions [in which to hold a fair vote] were absent, but the pragmatic decision was that having an imperfect election was better than having no election because that would be the end of the Dayton agreement," he said.
As it is, the international community now has its work cut out to try to push the peace process forward. A first step will be bringing the three new presidents to New York for the United Nations General Assembly.
Diplomats hope that international flattery, followed by hard cash, will persuade the new leaders - particularly the Serb and Croat members - that their future lies in a united Bosnia.