Theresa May is "frustrated" with international rules that stop British aid cash being used to help victims of Hurricane Irma and the UK was pushing to change them, Downing Street said.
Number 10 insisted the UK's aid effort had not been hampered by the rules set by the Organisation for Economic Cooperation and Development based in Paris (OECD).
But the Prime Minister's spokesman made clear Mrs May was not happy with the way the rules were operating and stressed that International Development Secretary Priti Patel was leading work to change them.
The spokesman said the OECD rules do not "stop Britain dedicating the money needed for the hurricane recovery and reconstruction effort".
"The response would have been just as large and swift regardless of the aid rules," the spokesman said.
But he added: "The Prime Minister is frustrated with the rules as they stand."
The UK has pledged a total of £57 million towards disaster relief and the public has helped to raise a further £1.3 million.
But an unnamed minister told the BBC the figure would have been significantly higher without strict international rules governing the allocation of the £13 billion aid budget, a claim disputed by Downing Street.
Anguilla, Turks and Caicos and the British Virgin Islands do not qualify for support from the pot because their incomes are too high.
The way Britain and 34 other developed nations spend their aid budget is governed by the OECD.
Countries are given a ranking according to need, which is intended to ensure the poorest countries take priority.
The UK is committed to spending 0.7% of national income on aid under the rules set by the OECD.
The Tory election manifesto committed to working to change the rules.
The Prime Minister's spokesman said: "We began detailed work after the election to change the rules to prevent precisely these kind of scenarios."
He indicated the UK could be prepared to act alone if there was no agreement on changing the international rules.
"What we are working on at the moment is changing the rules at the OECD, but the manifesto set out that if that wasn't possible we could look at changing the rules here and that remains the case."
During Business questions in the Commons, Conservative MP Philip Davies (Shipley) labelled the OECD "out-of-touch morons".
He said: "It's bad enough that we have a bloated and wasteful and unaffordable overseas aid budget but it's even more ridiculous that we now learn that we cannot spend our overseas aid budget on our overseas territories.
"As we are getting back control from the unelected and unaccountable European Union, can I suggest that we now get back control on our overseas aid spending from the unelected, unaccountable, out-of-touch morons at the OECD so we can spend our overseas aid budget on the things that we want to spend it on rather than the things that they tell us we can spend it on?"
Commons Leader Andrea Leadsom said the Government was "looking at how the current overseas aid rules apply to disasters" such as Hurricane Irma.