“Why would things be different in a general election?,” Mr Khan said.
Explaining his support for Mr Smith, he said the pair had agreed on the “big issues”, such as opposing the Iraq War.
Labour ‘suffering badly’
Mr Khan said: “Jeremy has already proved that he is unable to organise an effective team and has failed to win the trust and respect of the British people.
“Jeremy’s personal ratings are the worst of any opposition leader on record and the Labour party is suffering badly as a result.
“He has lost the confidence of more than 80% of Labour’s MPs in Parliament – and I am afraid we simply cannot afford to go on like this.”
Guide to the Labour leadership election
Mr Smith, the former work and pensions spokesman, is challenging Mr Corbyn for Labour’s top job, after the leader lost a no-confidence vote of his MPs in June.
MPs who voted against Mr Corbyn have criticised his leadership and his performance during the EU referendum, but supporters have argued that he has been undermined by his opponents in the party.
This week at a hustings event, Mr Corbyn insisted that he could reach out beyond his core supporters and win over “some people that have been tempted to vote Tory”.
But Mr Khan, who became mayor in May and has until now remained neutral in the leadership contest, said the EU referendum was a test for Mr Corbyn to get his message out, which he had “totally failed”.
He said that through the referendum and its aftermath, Mr Corbyn had “failed to show the leadership we desperately needed”.
“And you can’t just blame a ‘hostile media’ and let Jeremy and his team off the hook.
“I know from my own election – up against a nasty and divisive Tory campaign – that if we are strong and clear enough in our convictions, the message will get through to the public.
“That’s a test that Jeremy totally failed in the EU referendum. Why would things be different in a general election?
“His position on EU membership was never clear – and voters didn’t believe him.”
Explaining his backing for Mr Smith, Mr Khan added: “On the big issues Owen and I have been on the same side of the argument, including opposing the Iraq War.
“Owen led and – more importantly – won our fight against the Tories’ unfair cuts to tax credits and disability allowances, which would have hurt the most disadvantaged people in our society.”
Mr Smith said he was “hugely honoured” to have Mr Khan’s support.
“Sadiq ran a fantastic campaign to win power for Labour in London this year, securing a huge mandate from party members and the electorate,” he said.
“He showed that a vision of hope and optimism can win, if it’s backed up with a credible plan to deliver real meaningful change for people’s lives.
“Since that election we have already seen what a difference Labour can make when we hold power.”
Labour leadership election timetable
- 19-20 July: The number of MP nominations for each candidate was published
- 20 July: Deadline for people to sign up as a registered supporter closed
- 22 August: Ballot papers start to be sent out in the post (Labour Party members only) and by email
- 21 September: Deadline for ballot papers to be returned is midday
- 24 September: The result will be announced at a special conference in Liverpool
Speaking on Friday, Mr Corbyn said his message appealed “all across the country”.
He pledged to “win over people… by the policies we put forward”, such as decent housing and security at work, including “some people that have been tempted to vote Tory” in the past. The Labour leadership contest result will be announced on 24 September.