Nick Clegg has said people should not "fixate" on the timing of any investigation into whether culture secretary Jeremy Hunt broke the ministerial code in his dealings with News Corporation.
The deputy prime minister said he did not think it would be useful for "everyone to fall over each other and have lots of crossed wires and lots of independent inquiries and/or judge-led hearings".
The Labour Party has called on David Cameron to initiate an immediate independent inquiry into whether the culture secretary misled parliament.
Hunt's office has been accused of leaking sensitive information to News Corporation in order to help it in its bid to take over BSkyB.
But speaking on BBC Radio 4's World at One programme on Tuesday, Clegg said any inquiry should come after Hunt appeared before the Leveson inquiry.
"It's very unusual to have a member of cabinet before a judge under oath being subject to extensive questioning," he said.
"I think it is perfectly right, if after that evidence, there are question marks that have been raised ... then of course it is posible to have another supplementary inquiry."
He added: "please don't get fixated on precise chronology ... one way or another the full facts must and will be revealed."
Clegg's position is at odds with Lib Dem deputy leader, Simon Hughes, who has joined calls for there to be an immediate inquiry into Hunt.
Challenged over whether he had discussed the BSkyB takeover bid during a meeting with James Murdoch, he said: "I can't remember at all whether it was, can't remember at the time if that was in the offing."
"It's really insulting you think that the fact of a meeting implies culpability," he told the presenter.
The deputy prime minister was speaking just two days before the local elections. Tackled over his current personal popularity rating of -53%, Clegg said he had "given up trying to work out when my approval rating is good or bad".
"I think it's important, as leader of the party, I lead my party through thick and thin. Of course it is challenging to be in government when you are having to take responsibility for the painstaking job."