Mr Hague said Britain's preference was for Col Gaddafi to leave the country.
He was speaking in London ahead of bilateral talks with French foreign minister Alain Juppe about how to resolve the situation.
Mr Hague said the dictator's fate was "a question for the Libyans," saying it was not for France or the UK to determine the country's future.
He said the countries were "absolutely united" in their approach, following claims the French were growing impatient with the lack of military success.
The stance marks a shift in Mr Hague's approach. He has previously indicated that he wanted Col Gaddafi to leave Libya.
BBC diplomatic correspondent Bridget Kendall said the remarks come amidst signs the leadership of the Libyan opposition is no longer ruling out the idea that Col Gaddafi and his family could remain on Libyan soil.
This would happen as long as he gave up power and agreed to certain conditions, as part of a political deal to end the war.
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BBC diplomatic correspondent
William Hague's comments come at an interesting moment, as efforts are gathering pace to try to find a peace deal to bring the four-month military conflict in Libya to an end.
In the last few days Libyan opposition leaders have signalled that they are no longer ruling out the idea that Gaddafi could remain on Libyan soil, so long as he gave up all power and agreed to certain conditions, as part of a political deal to end the war.
Whether this shift will be enough to bring about a peace deal is still uncertain.
Several parallel mediation efforts are underway, involving UN, African and other envoys, as well as direct talks last week between pro-Gaddafi envoys and US officials.
So far any tentative plans appear to have stumbled over the crucial issue of how and when Gaddafi would step aside, and whether he would be allowed sanctuary from the arrest warrant issued by the International Criminal Court.
Mr Hague said: "What happens to Gaddafi is ultimately a question for the Libyans."
He went on: "What is absolutely clear, as Alain (Juppe) has said, is that whatever happens, Gaddafi must leave power. He must never again be able to threaten the lives of Libyan civilians nor to destabilise Libya once he has left power.
"Obviously him leaving Libya itself would be the best way of showing the Libyan people that they no longer have to live in fear of Gaddafi.
"But as I have said all along, this is ultimately a question for Libyans to determine."
Mr Juppe backed the foreign secretary's comments, saying the allies were in "perfect co-operation" in Libya.
He added: "We think that we must continue to exert strong pressure on the Libyan regime with the same methods.
"If we did not intervene four months ago it would have been a massacre in Benghazi and I think we may be proud to have taken this courageous decision."
On Sunday, British aircraft bombed a key intelligence building used by Col Gaddafi's forces, the Ministry of Defence said.
RAF Tornado and Typhoon aircraft attacked the Central Organisation for Electronic Research building in Tripoli.
The MoD insisted that it was a "wholly legitimate" target as it had long been used as a cover for the "nefarious activities" of the Gaddafi regime, despite being described as an engineering academy by the Libyan authorities.
More than 710 regime targets have been destroyed by the Royal Navy, Royal Air Force and Army Air Corps since military action began on 19 March, the MoD said.
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