Theresa May said the United Nations must reform or risk losing public support.
In her keynote speech at the United Nations General Assembly in New York, the Prime Minister said Britain will continue to be the second biggest contributor to the UN, but warned 30% of the annual £90 million core funding for the organisation's agencies would be ring fenced for agencies that showed "sufficient results".
Mrs May told the General Assembly that a failure to introduce reforms and make good on new secretary general Antonio Guterres's drive to make the organisation "more agile, transparent and joined-up" would jeopardise public support for the UN.
The shortcomings of the UN and ts institutions risk undermining the confidence of states as members and donors," she warned.
"If this system we have created is found no longer to be capable of meeting the challenges of our time, then there will be a crisis of faith in multilateralism and global co-operation that will damage the interests of all our peoples.
"So those of us who hold true to our shared values, who hold true to that desire to defend the rules and high standards that have shaped and protected the world we live in, need to strive harder than ever to show that institutions like this United Nations can work for the countries that formed them, and for the people who we represent.
"This means reforming our United Nations and the wider international system so it can prove its worth in helping us to meet the challenges of the 21st century."
In her keynote speech shortly before a private meeting with Donald Trump, the Prime Minister called on all countries to "come together and defend" the rules-based system of international agreements and conventions such as the Paris climate agreement which Mr Trump has threatened US withdrawal from.
Mrs May warned that the system was threatened by "states deliberately flouting for their own gain the rules and standards that have secured our collective prosperity and security".
She singled out Syria and North Korea, condemning the Assad regime's use of chemical weapons and Kim Jong-Un's highly-controversial nuclear weapons programme.
Mrs May met the US President minutes after delivering her speech. She said herself and Mr Trump had "had many discussions" on a variety of issues, including trade.
Mr Trump said: "It's great to have Prime Minister May from the UK and her representatives who are people who we know very well.
"We will be doing a lot of trading with the United Kingdom and we look forward to it.
"We've gotten to know each other over the last period of a year and it's a real honour to have you here."