The Education Secretary suggested that it was hypocritical of the Labour Party not to expect to have to answer important questions about Paul Flowers, whilst launching personal attacks against David Cameron.
Gove insisted there was no Conservative plan to fight a "dirty campaign".
He said: "I absolutely think that we need to have lots of questions: that's why the Chancellor of the Exchequer took the advice of independent people to set up an inquiry, which will ask searching questions about what went on right up to the moment that we discovered everything we discovered about Paul Flowers.
"The difficulty, I think, that Labour has is they were the people responsible for appointing/allowing Paul Flowers to be appointed on their watch."
Mr Gove said that when it came to answering questions over the Unite union official at the centre of the Grangemouth oil refinery dispute and the Falkirk vote-rigging inquiry, Labour "tend to clam up".
He added: "One thing that I think is slightly sort of off is that Ed Miliband has been a great advocate of transparency, judge-led inquiries, all the rest of it, but whenever anyone asks questions about the Labour Party, then he has a sort of coquettish reticence."
Asked if he would give his word that there were no plans to run a "dirty campaign", Mr Gove replied: "Absolutely."
Citing Damian McBride, Gordon Brown's disgraced former spin doctor, he said that while there had been "some disagreeable aspects of politics" in the past, the Tories were intent on running a "clean" election battle. However, he said Labour also needed to play fairly.
He told the BBC's Andrew Marr Show: "I think Ed Miliband wants to fight a clean election campaign. I certainly do. I know that David Cameron does.
"I think that the election campaign should be conducted on the basis of policy versus policy. My worry is that actually, so far, quite a lot of the critique of the Government from Labour has been very personal."
Members of Government had been "attacked for their background not for their beliefs," he said. "I think that's wrong."
"We are pushing forward social mobility, that's what matters more, I think, than where a politician went to school."