CAMBRIDGE, Mass. — As Boston celebrated Pride Week, an annual event honoring the L.G.B.T. rights movement that culminates in a parade, another event was drawing a flurry of attention on social media: a “Straight Pride Parade” that several men say they plan to hold in the city in late August.

Officials at City Hall said the organizers have yet to receive a permit for a parade, and it appeared uncertain this week whether the event, described on a website the organizers created, would actually take place. The group had earlier sought an application to raise a “straight pride” flag on City Hall’s flagpoles, a proposal city officials turned down.

It was also unclear whether the real intent of the event was a serious argument that straight Americans were oppressed and needed protection from discrimination, as the website suggests, or if it was meant to be a joke — and if so, what kind of joke.

One of the organizers, John Hugo, said in an interview that the intent was “lighthearted” and that the organizers bore no ill will toward gay people. One of the other organizers was gay, he noted, adding that the parade’s keynote speaker would be “a famous, prominent gay guy.”