TOKYO — For nearly three decades, millions of Japanese have clamored for their every album, lined up with breathless anticipation for their concerts and gathered on Monday nights for their hit television show.

Now, the nation is awash with anguish over word that SMAP — Japan’s longest-running boy band, if it can still be called that with its youngest member pushing 40 — is splitting up.

The news has dominated newspaper headlines and television talk shows since the band’s announcement this month. Even the governor of Tokyo and two members of Prime Minister Shinzo Abe’s cabinet have weighed in. One said he was worried about the effect on the Japanese economy, the world’s third-largest.

“We will not let them stop!” a grieving fan wrote in one of more than a dozen petitions on change.org pleading with the aging heartthrobs to remain together. “If we let them go and disband, it means Japan is finished.”