Mr Monti's surprise announcement on Saturday that he intended to resign early once next year's budget is approved has opened the prospect of an election in February, a few weeks before the natural end of his term in April.
Former Prime Minister Silvio Berlusconi, whose withdrawal of support for the technocrat government in parliament last week triggered the crisis, has already announced he will be running on a platform attacking Mr Monti's economic policies.
European Commission president Jose Manuel Barroso said Italy, the eurozone's third largest economy, remained at risk of a renewed bout of financial crisis, despite months of improving market confidence.
"The next elections must not serve as a pretext for putting in doubt how indispensable these measures are," he said.
"The relative calm on the markets does not mean we are out of the crisis," he said.
Mr Barroso's comments underlined the uncertainty created by the sudden acceleration of Italy's political crisis following Mr Berlusconi's decision to turn his back on Mr Monti, whose government his People of Freedom (PDL) party had backed in parliament for more than a year.
According to the daily Corriere della Sera, Mr Monti himself said he had been besieged with questions on the crisis while attending a conference in Cannes in the south of France on Saturday.
"I did not reply all day to the many questions which I received, especially from foreigners. I noticed their amazement about the Italian situation," he was quoted as saying. Italian 10-year bond yields, the main barometer of market opinion, rose last week as the crisis broke, reversing weeks of steady falls although they remain well short of the levels reached during last year's crisis.
The yield on the 10-year BTP stood at 4.5% at the end of last week, 323 basis points higher than the yield on lower-risk German 10-year Bunds, but much lower than the level of 7.3% seen last year.
Mr Monit, a former European commissioner, came to power at the height of the financial crisis a year ago and was widely credited with restoring Italy's credibility on financial markets and with European partners after the scandal-plagued Berlusconi era.