But on Wednesday, Bayrou had stinging words for both candidates, saying that Sarkozy, the conservative former interior minister, risked exacerbating social tensions in France while leftist Royal would worsen France's serious economic problems.
He said Sarkozy and Royal had both called him since Sunday's election, but he had not spoken to either of them.
"It will be worrying times for France if Sarkozy wins the presidency"
Be Humble, UK
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Bayrou said: "I will not give any advice on how to vote."
He announced plans for a new centrist party, with the provisional name of the Democratic Party, which would contest the parliamentary election in June and said he was ready for a public debate with both Sarkozy and Royal.
But, with a comfortable lead in the first round of the election, Sarkozy has less need of a swing and he said he was not interested in backroom deals.
'Anyone but Sarko'
"The electors don't belong to Francois Bayrou any more than they do to Segolene Royal, Jean-Marie Le Pen or Nicolas Sarkozy," Sarkozy told the daily Le Monde.
"Don't just reduce voters to their choice in the first round."
The latest opinion polls continue to give Sarkozy, the clear winner on Sunday, an edge, but a TNS Sofres poll commissioned by conservative daily Le Figaro and published in its Wednesday edition showed his lead down to just two percentage points.
|According to a survey by TNS Sofres, 46%|
of Bayrou's voters support Royal [Reuters]
Another poll by the Ipsos institute gave him a much more comfortable lead of some seven points.
In the April 22 first round, Sarkozy polled 31.2 per cent, Royal 25.9 and Bayrou 18.6 per cent.
With the campaign in its final stages, jobs, security and immigration are still the main issues, but the focus has moved more and more to personality.
The left is seeking to build on widely held concerns about Sarkozy's combative character and mobilise an "Anyone but Sarko" vote.
"Ten good reasons not to vote Sarkozy," the leftist Liberation splashed over its front page, following up with a litany of objections to Sarkozy's tough views on justice, the police, immigration, social welfare and power.
Although support for Royal is often tempered by doubts about her competence and reserves about her aloof personal style, surveys show even many conservative and centrist voters worry about Sarkozy, despite attempts to soften his style.
According to the TNS Sofres survey, 46 per cent of Bayrou's voters support Royal, against 25 per cent for Sarkozy and 29 per cent who have yet to make up their minds, although other polls have showed support roughly evenly split.