TV on the Radio bassist Gerard Smith has died of lung cancer, only a month after announcing that he was taking time off from the US art rock band to get treatment.

The band cancelled five upcoming tour dates in Detroit, Chicago, Minneapolis and Denver in support of their well-received fourth studio album Nine Types of Light, which debuted at No 12 in the Billboard charts.

The Guardian's review of the album said: "You only need hear opener Second Song – which somehow blends an alt-country melody with a cosmic funk chorus requesting 'every lover on a mission, shift your known position' – to realise this band are still light years ahead of their peers."

Smith joined the group full time in 2005, just in time to record their album Return to Cookie Mountain, which saw them break through to mainstream success. A message posted on the band's website said he had been diagnosed with cancer after their latest album was finished. He was 34.

The band wrote on their website in March: "Gerard has been undergoing treatment and will be unable to participate in the upcoming tour … [He] is fortunate enough to have health insurance and is receiving excellent medical care. We appreciate your concern and support for Gerard and his family."

His death has been announced in a statement on the site.

"We are very sad to announce the death of our beloved friend and bandmate, Gerard Smith, following a courageous fight against lung cancer. Gerard passed away the morning of April 20th, 2011. We will miss him terribly," reads the statement.