Mr Miliband blasted “delay and indecision” over how to deal with claims of inappropriate links between Dr Fox and his close friend, defence lobbyist Adam Werritty, and said the Prime Minister should have called in his independent adviser on ministerial conduct, Sir Philip Mawer.
But Mr Cameron said it would have been weak for him to jump to conclusions before knowing all the facts.
His comments came as the BBC broadcast fresh allegations that wealthy backers of Dr Fox funded Mr Werritty’s work and travel as he joined the Defence Secretary at meetings and conferences around the world over the past 18 months.
Questions have been asked over how Mr Werritty, who was Dr Fox’s flatmate and best man at his wedding, could have afforded his globe-trotting lifestyle and why he was present at meetings despite having no official position at the Ministry of Defence.
Speaking in Aberdeen, the Prime Minister said: “A strong leader actually recognises you have to take time to get all the information, answer all the questions, and then actually make a decision.
“A weak leader is someone who jumps at it because of some artificial deadline. Let’s get the facts established, and then we’ll make a decision.”
Mr Cameron said it was right to wait for Cabinet Secretary Sir Gus O’Donnell to complete his inquiry into the allegations, which is expected early next week after Mr Werritty has been interviewed for a second time.
Dr Fox insisted he was “back to complete normal working mode”, rejecting Labour claims that the furore over his friend was distracting him from his job.
The Defence Secretary yesterday cancelled a public appearance at a keel-laying ceremony in Barrow in order to attend a meeting of the National Security Council to discuss the latest situation in Libya.
“I’m continuing to do what is needed at the moment, which is that the Defence Secretary focuses on defence issues,” he told reporters.
But Mr Miliband said: “This uncertainty is not good for the country. We’ve got a distracted Defence Secretary and a distracted Government.”
The Labour leader and MP for Doncaster North said Mr Cameron was showing himself to be “a weak Prime Minister seemingly unable to make the right decision”.
Questioning why Sir Philip had not been called in, he added: “There is an issue now about delay and indecision at the heart of Government.
“A report should have been commissioned swiftly, and then a decision should have been made.
“He is showing ineffective leadership. He should have acted more swiftly, he should have done what the code says.”
But Mr Cameron said: “I think what is right is to allow the Cabinet Secretary Gus O’Donnell to complete his full report. I think we have to be patient and allow him to gather the information, to answer the questions and a judgment can be made.
“But let me repeat again, I think Liam Fox has done a good job in sorting out the defence budget, making sure we’re effective in Libya, and clearing up the mess in the MoD left by the last administration.”
Labour MP for Glasgow Central Anas Sarwar called on the Electoral Commission to investigate claims that Mr Werritty was effectively a privately funded adviser to the Defence Secretary.
If true, this would be a donation to Dr Fox which would legally have to be declared, he said.