Knightley and Mendes presented Massy Tadjedin's directorial debut "Last Night", a tale of trust, lust and deception also starring Sam Worthington and Guillaume Canet, to open the festival.
But the showing began almost two hours late.
Festival president and Italian actor Sergio Castellito, in a message explaining the demonstrators' demands, said, "We're no parasites or in constant need of help but a key part of an industry, the media industry, which is strategic for a modern country and involves more than 250,000 people."
"Last Night" director Tadjedin talked with demonstrators and said she was sympathetic to their demands. "We are pleased to renounce the red carpet and support you," she said according to the ANSA news agency.
Other hotly awaited films include John Cameron Mitchell's "Rabbit Hole" -- starring Nicole Kidman in the lead role and marking her debut as a producer -- which tells the story of a couple whose only child suddenly dies.
The festival, which runs from October 28 to November 5, also focuses on independent cinema, featuring films from countries including the United States, Mexico, Ireland, Denmark and Japan.
US director Martin Scorsese is to attend the premiere on Saturday of a digitally remastered version of "La Dolce Vita", renovated by the Gucci fashion house for the 50th anniversary of its release.
Gucci said it wanted to pay homage to Italian director Federico Fellini's masterpiece, starring Marcello Mastroianni and Anita Ekberg, for having paved the way for a new world with an obsession for style, fashion and celebrity.
"Oranges and Sunshine", the eagerly awaited debut by British director Jim Loach, son of veteran film maker Ken Loach, will be screened at the festival following its premiere in South Korea this month.
The film, shot on location in Nottingham, London and Adelaide, South Australia, is based on the scandal, discovered in the 1980s, of thousands of children deported without their parents' knowledge to Australia, where many suffered abuse.
Six works will have their world premiere, including a feature film on the adventures of London-based "nightmare investigator" Dylan Dog, the star of a popular Italian horror comic strip.
The festival, which has an annual budget of 13.5 million euros (18.7 million dollars), has received more support from 160 sponsors and is 70 percent self-financed, organisers said.
Fans of the "Back to the Future" trilogy are in for a treat as the festival plays host to an electric version of the iconic DeLorean car.
To celebrate the 25th anniversary of the trilogy, Enel and Wired magazine's Italian edition have converted a DeLorean to run on a 90-kilowatt engine powered by lithium-ion batteries.
The car, driven by a team from Wired, set off from Milan on Monday -- the day Marty McFly first travels back in time in Robert Zemeckis's film -- to arrive in Rome for the opening night of the film festival.