Mr Livingstone has been mayor since 2000
London mayor Ken Livingstone said he arrived 30 minutes late for a BBC radio debate because he needed to spend some time with his children.
His aides had suggested Mr Livingstone was late for the Asian Network debate because of hold ups on the Tube.
But when he did arrive Tory rival Boris Johnson said the Tube website showed "a good service in the Stratford area".
The mayor then said he left home late as his children "just wanted a little time this morning, sorry about that".
"Yeah, I'm very sorry. Look, my kids haven't seen me any evening this week and they didn't see me at the weekend and they just wanted a little time this morning, sorry about that," he added.
'Cannot be bothered'
Presenter of the Stratford-based debate Nihal Arthanayake asked: "Oh, so you actually left the house late?"
Mr Livingstone replied: "Yeah I left the house late. The kids were just... they don't understand why daddy spends more time with Boris than with them".
Mr Johnson said later: "He either cannot be bothered to show up to an important debate for London's Asian community or has to make up excuses to cover up for the fact the Tube doesn't run on time."
During the debate Mr Johnson was asked about an article he had written in 2002 in which he referred to "flag-waving piccaninnies" in Commonweath countries.
Mr Johnson said: "Piccaninny is an old-fashioned term for a young black child and yes I did use it and it is offensive and I've repeatedly apologised it."
He said he was writing it "in a satirical context" and said people wanted to hear about policies not "harping on bits and pieces from articles you can cull over 20 years of writing to demonstrate something that is simply not in my heart about what I think about race".
Mr Livingstone replied: "I don't think Boris is a racist, what Boris has been doing his entire political career is pandering to old people in the home counties and it never occurred to him he would have to run for election in London."
During the debate Mr Johnson also cited his Turkish heritage and told the debate's host: "You can't out-ethnic me."
Asked who his favourite Bhangra artist was, he said he could not remember but added: "My children are quarter Indian - so put that in your pipe and smoke it."
Mr Paddick, who was highest-ranking openly gay police officer in the UK, was asked how he would win over people who considered his lifestyle "sinful".
He replied: "The fact is the previous (Metropolitan Police) commissioner was very reluctant to put me into Brixton because he thought they would be a homophobic backlash by the black and Caribbean community.
"Fifteen months later they were demanding my reinstatement when I was removed as a police commander.
"At the end of the day people realise I'm a decent man, I'm honest, I do a good job, I listen to people, my sexuality becomes a secondary issue."
Mr Livingstone and Mr Johnson refused to discuss their private lives, arguing voters were not interested.