The attack came in the Commons as Tories claimed Mr Livingstone had warned that his local Brent LBC would have to cut£2.4 million from education because of this year's local government settlement.
Ms Armstrong replied: 'It's not my job to account for the meanderings of Mr Livingstone and indeed I am not responding to his electioneering.'
Supporters of Mr Livingstone took out a three-quarter page advertisement in Monday's Guardian amid fears that Labour bosses will veto Mr Livingstone's bid to be the party's official candidate.
Mr Livingstone has said legal action is a possibility if he is excluded from the list of candidates. 'Broadly, one of the 69,000 members of the Labour Party could take the point to court saying they have been denied the chance to vote for me. I should think you'll find someone who is going to give it a try.'
Another expected mayoral candidate, TV presenter Trevor Phillips, has quit London Weekend Television's Crosstalk current affairs show. LWT said Mr Phillips was stepping down to avoid any conflict of interest that could arise if he was campaigning to be London mayor.