Tarpischev was fined $25,000 and suspended from tour involvement for a year after referring to Serena and Venus Williams as "brothers" on a Russian TV show and called them "scary" to look at.
Asked whether he regretted his comments, Tarpischev told The Associated Press at the Kremlin Cup that the program on which he spoke was "a humorous show," adding: "I don't answer stupid questions."
When asked about his ban, Tarpischev said: "I can't comment. I don't understand it."
In a statement released later by the Russian Tennis Federation, Tarpischev denied any "malicious intent" and said his quotes had been taken out of context.
"I didn't want to offend any athlete with my words," he said. "I regret that this joke ... has garnered so much attention. I don't think this incident deserves so much fuss."
The Williams sisters are "outstanding athletes" who "personify strength and perseverance," he added.
The WTA said it would seek his removal as chairman of the Kremlin Cup tournament, which ends Sunday.
Russian Sports Minister Vitaly Mutko told the ITAR-Tass agency that he regretted that Tarpischev had made the comments and that his suspension was "an unpleasant fact," but suggested his sanction should be reduced.
"It's probably worth trying to get the punishment softened," Mutko said.
Tarpischev has been chairman of the Kremlin Cup, Russia's only WTA event, for all of its 18 years as a women's tour event, and is also a member of the International Olympic Committee. During the 1990s, he was the personal tennis coach to Russian President Boris Yeltsin and served as his adviser on sports matters.
He made his comments during an appearance on a Russian talk show this month alongside former Olympic singles champion Elena Dementieva. When Dementieva was asked what it was like playing against the Williams sisters, Tarpischev interjected and called them the "Williams brothers." He also said that "it's scary when you really look at them."
The WTA tour issued a sharp rebuke on Friday.
"Mr. Tarpischev's statements questioning their genders tarnish our great game and two of our champions," WTA Tour chairman and CEO Stacey Allaster said in a statement. "His derogatory remarks deserve to be condemned and he will be sanctioned."