Jack Black has put his rock duo Tenacious D on hold following an onstage comment made by his bandmate Kyle Gass, which seemed to support the assassination of Donald Trump.

Gass was celebrating his birthday during a concert in Sydney on Sunday, with a cake presented to him on stage. Black told Gass to make a wish as he blew out the candles, and Gass responded, to audience laughter, “Don’t miss Trump next time” – a reference to the failed assassination attempt by 20-year-old Thomas Matthew Crooks at a Trump rally the previous day.

Black continued with the concert following Gass’s comments, but has now put out a statement:

I was blindsided by what was said at the show on Sunday. I would never condone hate speech or encourage political violence in any form. After much reflection, I no longer feel it is appropriate to continue the Tenacious D tour, and all future creative plans are on hold. I am grateful to the fans for their support and understanding.

Tenacious D had been due to perform four more dates across Australia before travelling to New Zealand.

An Australian senator, Ralph Babet, had called for the band to be removed from the country, saying on Tuesday: “I call on the prime minister Anthony Albanese to join me in denouncing Tenacious D, Jack Black and band member Kyle Gass, and I call on the immigration minister Andrew Giles to revoke their visas and deport them immediately. Anything less than a deportation is an endorsement of the shooting and the attempted assassination of Donald J Trump.”

Tenacious D have spliced together comedy and classic rock for over 30 years, with the creative partnership of Black and Gass dating back even longer, to the mid-1980s when they were both performers in the Actors’ Gang theatre troupe. They began writing music together, gave their debut performance in 1994, and became much-loved by the rock bands they somewhat lampooned, earning support slots with Tool, Foo Fighters and others.

A crossover into TV was short-lived, but as Black’s acting career took off, the band were signed to a major label and released their self-titled debut album in 2001, which gradually became a platinum-selling success in the US (and two times platinum in the UK). Their second album The Pick of Destiny was paired with feature film Tenacious D in the Pick of Destiny, and the band have released two further studio albums. 2012’s Rize of the Fenix was their biggest chart hit, reaching No 2 in the UK and No 4 in the US.

Prior to their Australian tour, Tenacious D played arenas across the UK earlier this year. The Guardian’s Dave Simpson gave their Manchester concert a four-star review, calling it “a parody of a rock show that’s a great rock show in itself”.

The Guardian has contacted representatives for Tenacious D for comment from Gass.