Theresa May’s spokesman refused to comment explicitly on the incident as Essex Police are investigating.
But he said the prime minister was “clear” she condemned racial abuse.
“When people are travelling and going about their public life, no-one should be subjected to intimidation or any form of abuse,” the spokesman said.
“The Prime Minister has always been clear that racial abuse is abhorrent.
“In relation to this particular case, there’s obviously an investigation being conducted by Essex Police and it’s right that I don’t comment specifically on that.”
A video of the original outburst was posted online on Friday afternoon.
It showed a row break out as flight from Barcelona to Stansted prepared to take off.
The victim, 77-year-old Mrs Gayle, was defended by her daughter, who told a man sitting next to them that her mother was disabled.
He replied: “I don’t care whether she’s f****** disabled or not – if I tell her to get out she gets out”.
The unidentified man then called her an “ugly f****** c***” and threatened to “push” her to another seat unless she was moved.
The passenger, who has not been named, then shouts “don’t talk to me in a foreign language you stupid ugly cow” before calling her an “ugly black b******”.
Ryanair has come under fire from social media users for staff failing to reprimand the man or remove him from the plane.
The Gayle family has told Sky News that Ryanair has not been in touch with them since the incident.
Labour’s shadow home secretary Diane Abbott responded: “Surely Ryanair should be contacting this woman and apologising for the racist abuse she suffered?”
Fellow Labour MP David Lammy has also called for travellers to boycott the airline in protest.
“It’s 63 years since Rosa Parks said ‘no’ to sitting on the back of the bus and we ain’t going back,” he said.
Transport Secretary Chris Grayling said the comments were “totally unacceptable”.
“The fact is that abuse of that kind, race abuse of that kind, is a crime – and if a crime is committed it should be dealt with appropriately,” he said.
“And so therefore I would hope, notwithstanding what took place on that day, that police would want to take action in such an extraordinarily unacceptable case.”