They were asking UN. NATO just formed a coordination and command body for a coalition of 19 countries which had some interests in Libya.
That's how the UN works.The UN has zero standing forces. They have two paths to military intervention;
1) Calling for peacekeepers under a UN flag.
2) Authorising a third party to intervene.
Calling for peacekeepers is an incredibly complicated procedure. The level of peacekeepers (size and strength of the force) must be agreed on by the host nation. In this case they would have needed Gadaffi to sign off on how many troops were deployed and how much kit they brought. Once that was agreed on a call would go out for troops to be committed by different nations to form part of the force. Until and unless the precise size of the force agreed on can be reached not one body can be deployed.
Such peacekeeper forces are the only explicitly UN forces available.
Authorising action is far more likely and usually has more direct effect. In this case the UN authorised the plans put forwards by, among others, France, the UK and US, in response to the calls from the Libyan rebels and diplomats.
By the way, IIRC Gadaffi even wrote the letter to Obama saying something like "Son, let`s fight terrorism together!" and generally was ready for the negotiations. Some more agressive diplomacy would have been enough to topple the regime without a drop of blood hitting the ground, but instead of this NATO chose the violent way again.
Lets be serious here. Gadaffi has serious history when it comes to bullshitting. He has said pretty much everything imaginable at some point. But more importantly he has had a history of sponsoring terrorism. He had zero credibility when it came to negotiation, especially while still attacking civilians.
Hell, Gadaffi declared a ceasefire after the resolution was passed. At that time no missiles had been fired by NATO or any other outside forces. However, he continued artillery attacks against opposition groups. It was when tanks rolled into Benghazi that France (at that time not under the NATO flag) started the attacks.
France took that action because the UN's resolution required any steps short of an invading foreign ground force in order to protect civilians and civilian-populated areas. Basically they were under UN orders to stop civilians being killed by any means.
Drawing a line here between the UN and NATO/the coalition is false. You can argue against the intervention on other terms, but saying NATO=EVIL doesn't really get anywhere.