Another US cinema chain, Carmike, announced that it had cancelled all screenings of the film, which is due for release across the US on Christmas Day.
At the Los Angeles premiere of The Interview on 11 December, Mr Rogen, who also co-directed the film, thanked Sony Pictures chairman Amy Pascal for "having the balls" to back it.
The studio chief has been personally embarrassed by the hacks, after multiple emails from her own account were published online. Yesterday, Mr Rogen and Mr Franco both cancelled all their upcoming media engagements in support of the film.
The latest threat from the GOP comes a day after hackers leaked a scene from The Interview, depicting the death of the North Korean leader in a rocket attack.
During the summer, the North Korean regime warned that the film's release was "an act of war" that would lead to "merciless" retaliation. Although there is no firm evidence to connect North Korea to the hackers, it now seems clear The Interview provided a motive for the cyber-attack.
The Department of Homeland Security said in a statement that there was "no credible intelligence to indicate an active plot against movie theatres," while the FBI said it "continues to work collaboratively with our partners to investigate this matter."
On Tuesday the hackers also released a cache of some 8,000 emails from the account of Michael Lynton, the CEO of Sony Entertainment, describing its latest data dump as part of a "Christmas gift".
The Sony data breach is one of the largest in US corporate history. On Monday evening, two former Sony Pictures workers filed a lawsuit against the firm for failing to prevent the hack - and therefore the theft of personal and financial information from past and current employees - despite warnings that it was vulnerable to such an attack.
Meanwhile, human rights group Fighters for a Free North Korea has announced plans to airlift DVD copies of The Interview into the country by floating them over the border attached to hydrogen balloons. Thor Halvorssen, the philanthropist funding the initiative, told the Hollywood Reporter, "comedies are hands-down the most effective of counter-revolutionary devices."
- Independent