Theresa May takes veiled swipe at Donald Trump over his climate change stance during UN speech in New York

Prime Minister Theresa May has delivered a veiled swipe at Donald Trump over his demand to renegotiate the Paris Agreement on tackling climate change.

In her keynote speech to the United Nations General Assembly in New York, the PM called on all countries to "come together and defend" the rules-based system of international agreements and conventions such as the Paris accord and nuclear non-proliferation treaties.

It came shortly before a private meeting with the US president at the Lotte Palace Hotel.

Mr Trump's call for the Paris accord to be rewritten in America's favour was rejected on Tuesday by French president Emmanuel Macron, who told the UN that "we won't go back" on the 2015 deal which sets out mechanisms to keep global warming within two degrees of pre-industrial temperatures.

Without mentioning Mr Trump or the US by name, she made clear that she regards it as vital that all UN states stick by their commitments in agreements to tackle issues ranging from security to trade protectionism and climate change.

"I believe that the only way for us to respond to this vast array of challenges is to come together and defend the international order that we have worked so hard to create and the values by which we stand," said Mrs May.

"For it is the fundamental values that we share - values of fairness, justice and human rights -that have created the common cause between nations to act together in our shared interest and form the multilateral system.

"And it is this rules-based system which we have developed - including the institutions, the international frameworks of free and fair trade; agreements such as the Paris Climate Change accord and laws and conventions like the Non-Proliferation Treaty - which enables the global co-operation through which we can protect those values."

Foreign Secretary Boris Johnson was in the audience for Mrs May's speech shortly after her spokesman revealed they would travel back to the UK together before a special Brexit Cabinet session on Thursday.

Mr Johnson's Telegraph article on Saturday laying out his personal demands for Brexit has overshadowed Mrs May's three-day visit to the US and Canada in the run-up to her crucial Brexit speech in Florence on Friday.

In her speech, Mrs May also singled out Syria and North Korea for condemnation as she 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".

Security Council members should be "prepared to take all necessary measures" to exert pressure on Kim Jong-Un and restore stability to the Korean peninsula, she said.

She also specifically condemned the "unforgiveable" use of chemical weapons by Bashar Assad's regime in Syria and the "outrageous" development of nuclear weapons by North Korea.

The PM also called on the United Nations to reform, warning that Britain will make up to 30 per cent of its annual £90 million core funding for the organisation's agencies conditional on it making good on new secretary general Antonio Guterres's drive to make it "more agile, transparent and joined-up".

While the UK will continue to be "generous", the £30 million will be provided only to agencies which show they are efficient and transparent.

International Development Secretary Priti Patel announced on Tuesday that the UK was introducing a 30 per cent "performance agreement" under which core funding for the UN will be dependent on improved results, including effective accountability and feedback on how money donated in response to global emergencies is spent.

Mrs May told the General Assembly that a failure to introduce reforms along the lines proposed by former Portuguese prime minister Mr Guterres would jeopardise public support for the UN.

Reform will require better co-operation on the ground between UN agencies, improvements to gender equality and real leadership on tackling damaging issues like sexual exploitation and abuse by UN workers on missions in disadvantaged countries, she said.