According to reports in the Italian press, Luti stepped down amid fears that this year's fair would be diminished due to fewer exhibitors and attendees.
Common purpose "has failed"
"The common will of purpose [...] has failed," he said.
The furniture fair is due to be held in Milan from 5 to 10 September, after it was moved from its traditional April slot due to Covid-19.
However, doubts have been swirling in recent weeks over whether the fair would be forced to cancel for a second year in succession.
Resignation "a painful choice"
"Leaving the presidency of the Salone in such a delicate and complex moment is a [..] painful choice," La Reppublica reported Luti as saying.
"Over the years I have worked hard to affirm the event as a representation of the system at an international level, but there are no longer the conditions to pursue my vision of compactness in the sector for the common good."
Luti resigned on Thursday ahead of a board meeting of FederlegnoArredo, the Italian timber-trade body that owns the Salone del Mobile brand.
His departure comes just a few days after the Italian government announced plans to lift some Covid-19 restrictions and allow trade fairs to take place once again from 1 July.
Government gave assurances
On the surface, this seemed to satisfy the demands of the Salone del Mobile, which had been pressing the government for reassurances that would allow it to push on with plans for its September event.
Luti hoped the news would lead wavering exhibitors to commit to the event.
"The Salone del Mobile di Milano is an immeasurable asset for the entire country, and the government has confirmed that it is fully aware of this," Luti said last week following a series of meetings with the government ahead of its announcment.
"Most importantly, this has to be a mindset shared by the companies who have to confirm their attendance at the trade fair, as a key driver of recovery in the furnishing sector, the Italian economy and society."
However, Luti's resignation makes it clear that the measures announced by prime minister Mario Draghi and health minister Roberto Speranza were not enough to unite stakeholders behind his vision for the fair.
Bookings from exhibitors are thought to have been down and overseas visitors seem unlikely to travel to Italy in large numbers, leading to tensions among key partners and rumours that leading Italian brands have cancelled their booths.
"I respect everyone's decisions but I do not share the desire not to team up in such a delicate moment and to at least give up trying to define a concrete path to do what could be the symbol of the country's recovery," Luti is reported to have said.
"I certainly recognise the difficulties and also the unknowns that prevent us now from clarifying all the uncertainties given by the still looming pandemic scenario. But what matters to me is the common will of purpose, which has failed."
Fuorisalone will go ahead
The annual Salone del Mobile is the world's biggest and most important furniture fair, attracting 386,236 visitors from 181 countries when it was last held in 2019.
Earlier this month, organisers of Milan's fuorisalone events banded together to declare that they will host their shows regardless of whether the Salone del Mobile goes ahead.
The image of Claudio Luti is courtesy of Salone del Mobile.Milano.