United Continental Holdings was the biggest faller on the S&P 500 index at the opening bell.
But it started to pare losses in afternoon trading and was given a further boost by a second statement from Mr Munoz.
The footage taken inside the airliner shows a man being pulled out of his seat and dragged down the aisle. He is later seen with blood on his face.
Communications experts have predicted the incident could damage United Airlines' brand.
It comes just weeks after the company, whose slogan is "Fly the Friendly Skies", was criticised on social media for refusing to allow two teenage girls to board a flight because they were wearing leggings.
Wall Street jitters
The recovery in the United share price came as US stocks narrowed their losses in afternoon trading.
Wall Street shares were hit by investor nerves over geopolitical tensions between the US and Russia over Syria.
The S&P 500 share index itself finished 3.38 points lower at 2,353.78.
The Dow Jones fell 6.72 points to 20,651.30, while the tech-focused Nasdaq index ended 14.15 points lower at 5,866.77.
Investors sought out so-called safe haven assets, with gold gaining 1.6% to $1,274.26 an ounce and the Japanese yen rising 1% against the dollar.