David Cameron has said he will not take any lectures on dealing with Libya from Labour in Commons clashes on the government's response to the crisis.
The PM said William Hague was an "excellent foreign secretary" amid attacks from Labour leader Ed Miliband.
Mr Miliband said the "flights fiasco", comments by Mr Hague and a failed SAS mission had raised questions about the government's "competence".
The PM said the UK had led the way in getting a tough UN resolution on Libya.
Fighting continues between forces loyal to Colonel Muammar Gaddafi and those seeking to end his 41-year rule over Libya, three weeks after hostilities began.
Mr Miliband said there had been a series of mistakes by the UK government in the way it had dealt with events in Libya - including delays getting UK nationals out of the country, Mr Hague's remarks that Libyan leader Col Muammar Gaddafi may have left the country for Venezuela and "overblown briefing" about potential military action and the SAS "set back".
He said there was an "issue of competence at the heart of this government".
"Does the prime minister think it is just a problem with his foreign secretary, or is it a wider problem in his government?"
Mr Cameron replied: "I'm not sure I particularly want to take a lecture from Labour about dealing with Gaddafi and dealing with Libya, I think the first thing we should have from the Labour Party when it comes to Libya, Gaddafi and the release of [Lockerbie bomber Abdelbaset al] Megrahi is an apology."
He said the UK had "led the way" in getting a tough UN resolution on Libya and on making sure the world was preparing for every eventuality - including a possible no-fly zone.
When Mr Miliband suggested there had been "deafening silence" about the conduct of Mr Hague, Mr Cameron hit back with a jibe about Mr Miliband beating his brother David - a former foreign secretary - to the Labour leadership.
"I think we have an excellent foreign secretary and when it comes to it, there is only one person I can remember round here knifing a foreign secretary."
Mr Hague was not in the Commons at the time because he was briefing the Queen, according to the Foreign Office.
Mr Miliband, who also attacked Mr Cameron over police cuts, suggested he did not "have a clue what's going on out there... the prime minister may act like he is born to rule but the problem is he is not very good at it".
Mr Cameron replied by quoting David Miliband's speech on Tuesday in which he said parties of the left were losing elections because they had a "deficit of ideas".
There was much speculation about Mr Hague's future in the newspapers following his lengthy response to questions about his position on Tuesday in which he said during such momentous times "all of us who have taken on the job of shouldering responsibilities at this time must see those responsibilities through for an extended period of time in the face of any criticism or setbacks".
BBC political editor Nick Robinson said that response, and a flat performance in the Commons on Monday, had prompted questions about Mr Hague's enthusiasm for the job.
He added that Mr Cameron had faced a dilemma in answering Mr Miliband because he did not want to fuel the speculation about Mr Hague further.
Cabinet Office minister Francis Maude told BBC Two's Daily Politics that he disagreed with newspaper criticism of Mr Hague's performance and said he had "statesmanship, gravitas and authority". He said he was "on top" of what was a "very tough job".
Pro-Gaddafi forces have been stepping up their counter-offensive and there have been reports of heavy shelling and considerable loss of life in Zawiya, which fell to rebels two weeks ago.
Earlier, Tory backbencher Mark Pritchard has said the international community should allow rebels access to arms - he has previously suggested they be allowed limited numbers of surface-to-air missiles - to allow them to defend themselves.
He said pro-Gaddafi forces had an "overwhelming advantage" and without swift action would retake lost ground.
Weapons should not come direct from Nato but could be channelled through a third country or funds provided to help rebels buy them, he suggested.
The UK and France are working on a UN resolution for a no-fly zone but the US has cautioned that it must be a UN decision with wide international support.
Col Gaddafi has said his people will take up arms if one is imposed by Western nations or the UN, as many of the rebels have been calling for.
In an interview with Turkish TV on Wednesday, he said a no-fly zone would show the true intention was to seize Libya's oil.