Italy's Five Star Movement leader on Monday called on supporters to protest peacefully, a day after a standoff with the president forced it to abandon efforts to form a coalition government with the far-right Lega.

"Let's not give up now, we must not give in to the arrogance of the institutions which have decided to keep people from making decisions for their own country," Luigi Di Maio said, speaking live on Facebook.

"Make some noise, it is important that we do so all together," Di Maio added.

The 31-year-old leader said the anti-establishment group would organize peaceful walks and rallies in all Italian cities, including an event in Rome on June 2 - a national holiday celebrating when the country became a republic in 1946.

He also reiterated the group had never planned for Italy to exit the euro zone.