The German conservative politician was questioned for nearly three hours by three EU parliamentary commissions amid demands that he be punished for the comments, for which he has already apologized.
"I regret these remarks," Oettinger said, as he spelt out measures to reinforce protection for minorities.
"In the weeks to come I want to publish a statement on diversity and inclusion," he said, referring especially to sexual orientation.
He also praised a "very important" objective, introduced by his predecessor, to see at least 40 percent of managerial posts at the commission filled by women by 2019.
Oettinger, previously the digital services commissioner, was named in October by commission chief Jean-Claude Juncker to take over the budget and human resources portfolio from Kristalina Georgieva, a Bulgarian, who left for the World Bank.
But less than a month later, Oettinger was forced to apologize for referring to Chinese people as "slitty eyes" and making disparaging remarks about women, gay marriage and Belgian politicians in a speech.
He had joked that German politicians could introduce mandatory gay marriage.
Oettinger also stirred up controversy in 2014, before becoming digital commissioner, when he criticized female celebrities whose naked photos were stolen, stating "if a celebrity is stupid enough to take a nude photo of themselves and put it on the Internet, then they can't expect us to protect them."
But German media pointed out that the photos were not posted online, but rather hacked by criminals, suggesting that the situation was "too challenging for him".
Oettinger got into hot water again last year over accepting a lift in a Kremlin lobbyist's private jet to Budapest without reporting it under disclosure rules.
In his address to the EU parliament's budget control, budget affairs and judicial affairs commission, Oettinger said he considered himself "independent of lobby groups" and open to improving transparency rules.
The Euro-parliamentarians questioned Oettinger about his new role but not about his aptness for it. As he was already an EU commissioner, the session was formally an "exchange of views" rather than a panel of inquiry or an approval procedure.
Not all the EU parliamentarians present were satisfied.
Pascal Durand of the parliament's Green group said Oettinger's behaviour "calls for sanctions" rather than "promotion."
"The Oettinger affair is a classic case of everything you need to destroy the legitimacy of a political institution," said Durand.
The Eurodeputies involved will make their official consultative remarks in a later letter.
Ten European grassroot and watchdog groups, including Transparency International, Oxfam and Corporate Europe Observatory, last week called on lawmakers to oppose Oettinger's appointment.
"Commissioner Oettinger has made racist, sexist and homophobic remarks on several occasions in the past, most recently at a speech he gave in an official capacity in Hamburg on 26 October," they said in a joint letter.
"In our view, Commissioner Oettinger is not the right person for this task."