TEHRAN — Mixing exhortations of death to America with admonishments to children about healthy teeth and gums, Iran celebrated the 35th anniversary of the Islamic Revolution on Tuesday, and the state news media said millions had exuberantly participated.

At the largest rallies, here in the capital, the talks on Iran’s disputed nuclear program with world powers, including the United States, dominated the event, traditionally organized by hard-line factions that have shown strong skepticism about the negotiations.

Posters and placards were distributed bearing slogans that referred to Secretary of State John Kerry’s recent remarks that despite the discussions, the military option remained on the table for resolving the dispute over the nuclear program. Iran contends it is pursuing atomic power for peaceful purposes, but many other countries, notably the United States and Israel, suspect its nuclear program is intended to camouflage the production of nuclear weapons.

“We are eager for all options on the table,” many of the placards read, cheerfully hoisted by Iranian parents pushing baby strollers while shouting, “Death to America!” Other posters read, “We are ready for the great battle.”