Pardee was 76.
Bassity said Monday that Pardee's son Ted confirmed the death to him.
Pardee's family announced that he had gall bladder cancer that had spread to other organs and that he had six to nine months to live in November.
Pardee was inducted into the College Football Hall of Fame in 1986.
"Today, we mourn the passing of a great man who dedicated his life to the game of football and was a true gentleman in every sense of the word," Houston athletic director Mack Rhoades said.
"It was not a coincidence that success followed coach and his teams wherever he worked, and the University of Houston program was blessed to have him lead our football program during some of our most exciting times."
He survived a bout with melanoma when he was 28 and in the middle of his 15-year NFL playing career.
He played six-man football at Christoval High School in west-central Texas, near San Angelo, before moving on to Texas A&M. Bryant became the Aggies' coach in 1954 and moved their preseason camp to desolate Junction, about 100 miles northwest of San Antonio.
The state endured a severe drought and an historic heat wave that year, but Bryant worked his team through the brutal conditions and refused to allow water breaks in an effort to toughen players. Pardee was one of 35 players who made it through to the end of the 10-day camp without quitting.
Pardee played three seasons at Texas A&M and was the 14th overall pick in the 1957 NFL draft by Los Angeles. He played for the Rams from 1957-64, sat out a year to deal with his melanoma, and played seven more seasons. He finished his playing career with the Washington Redskins in 1973.
He was selected as an All-Pro in 1963 and 1971.
He coached in the World Football League for one season before moving on to NFL coaching. He was the Chicago Bears' head coach from 1975-77. He coached the Redskins from 1978-80 and was fired after Washington went 6-10.
He served as San Diego's defensive coordinator for one season, then returned to Texas to coach the USFL's Houston Gamblers.
When the USFL disbanded in 1987, Pardee became the coach at the University of Houston and brought along the fast-paced "Run-and-Shoot" offense that worked well with the Gamblers.
The NCAA levied severe sanctions on the program in 1988, the result of violations committed under previous coach Bill Yeoman. Houston was banned from playing in a bowl game for two years and banned from playing on television in the 1989 season.
But the Cougars led the nation in total offense (624.9 yards per game) and passing offense (511 yards per game) in 1989, and quarterback Andre Ware became the first black quarterback to win the Heisman Trophy. Houston finished 9-2 and ranked No. 14 in the nation.
"When you talk about the great offenses in the history of college football, coach Pardee's Run-and-Shoot teams from the late 1980s must be considered near the top of that list," Houston coach Tony Levine said.
"We continue to feel the impact from his innovative ideas and leadership of those teams in college football today, and our thoughts and prayers go out to all his family and friends."
His Houston teams were a precursor to the high-flying offenses now common in college football. He coached the Cougars to a 95-21 win over a just-back-from-the-NCAA-death-penalty SMU team in 1989.
The Cougars became the first team in NCAA history to finish with more than 1,000 yards of offense, as they piled up 1,021 yards in the win where Ware was on the bench by halftime.
Pardee became the coach of the NFL's Houston Oilers in 1990, and led the team to the playoffs in each of his first four seasons. Oilers owner Bud Adams traded star quarterback Warren Moon to Minnesota before the 1994 season, and Pardee resigned after a 1-9 start that year.
He ended his NFL coaching career with a record of 87-77.
His last coaching job came when he worked for the Birmingham Barracudas of the Canadian Football League in 1995.
His name emerged several years later for the Houston job, but the school hired Kevin Sumlin instead. Ted is the color analyst for Houston football radio broadcasts.
Houston announced that his family had established the Jack Pardee Memorial Scholarship Fund at the school in his honor. The scholarship will be awarded annually to a walk-on player on the football team.
"When my father was diagnosed back around Thanksgiving, we were able to have many great conversations about the past and the future," Ted said in a statement.
"One conversation was around what his lasting legacy would be. He truly loved the time spent at the University of Houston and wanted to find a way to help a deserving, hardworking, dedicated athlete who might not have the means to pay for their own college tuition. He could have offered his name to a lot of different charities or scholarship funds, but this was what my dad wanted to do."
Pardee and his wife, Phyllis, were married for more than 50 years and have five children and 12 grandchildren.
Funeral arrangements were pending Monday night.
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