Maurice Gibb, 53, died Sunday after four days in the hospital for an intestinal blockage. He underwent surgery Thursday, and before that, the hospital reported he had undergone cardiac arrest.
"The fact that they had to operate on Maurice during the shock of cardiac arrest is very questionable," said his older brother, Barry Gibb, 55.
"We will pursue every factor, every element every second of the time line of the final hours of Maurice's life. We'll pursue that relentlessly. That will be our quest from now on," he said.
Officials at the hospital said they could not comment Monday.
"We're aware of the situation -- of the reports in the media," said Kathleen Dorkowski, a spokeswoman for Mt. Sinai Hospital. "We are limited by privacy laws. We are not allowed to discuss the treatment of any of our patients. We have to follow those regulations."
Maurice Gibb sang and played keyboard for the Bee Gees, who produced six No. 1 singles from 1977 to 1979, including "Stayin' Alive." The group's last Top 40 hit was "This is Where I came In" in 2001.
"One thing I will tell you is that the Bee Gees will go on," Barry Gibb said.
"All I can tell you was he was one of the most beautiful people in the world, and a very gifted man. And it's a loss to the world," said Robin Gibb, Maurice's twin brother.
Although closely associated with the disco beat since "Saturday Night Fever" days, the Bee Gees' tightly locked falsetto harmonies have been an instantly recognizable presence on the airwaves for five decades, earning seven Grammy awards and more than 110 million sales.
Their career record sales add up to the fifth largest total, behind the Beatles, Elvis, Michael Jackson, and Paul McCartney singing alone.
The family lived in Manchester, England, and moved to Brisbane, Australia -- where the then teenage boys adopted the "Bee Gees" moniker as their music career was taking off.
Using the proceeds of their first hit record, they moved back to England in 1966 where their manager was Robert Stigwood, a partner of the Beatles' manager Brian Epstein. They finally settled in the 1970s in Miami Beach. At one point they broke up, but got back together in 1974.
The youngest of the four brothers, Andy, had had his own hits in the late 1970s but did not sing with the group. He died of a heart infection in 1988, at the age of 29.
Notable deaths of 2014 [PHOTOS]