Donald Trump has accused Hillary Clinton of "allowing North Korea to research and build" nuclear weapons, after the former election rival criticised his opening speech to the UN General Assembly.

The President's comments came after Ms Clinton called his address to the General Assembly “very dark, dangerous”, and “not the kind of message that the leader of the greatest nation in the world should be delivering” while appearing on Stephen Colbert's The Late Show.

The President chose to attack Ms Clinton on Twitter the next morning, claiming: “After allowing North Korea to research and build Nukes while Secretary of State (Bill C also), Crooked Hillary now criticises.”

He then retweeted a comment from an account called “EaglePundit”, which alleged that she and former President Barack Obama effectively gave nuclear weapons to North Korea.

“It is the height of hypocrisy. Obama and Clinton in effect gave nuclear weapons to North Korea by their policy of appeasement,” the tweet read.

Ms Clinton made her remarks in the wake of Mr Trump's first address to the UN General Assembly. When asked what she made of the President's speech, the former Secretary of State said: “You are both required to stand up for the values of what we believe in – democracy and opportunity – as a way to demonstrate clearly the United States remains the beacon that we want it to be,” adding that even dangerous situations such as that of North Korea should be led with diplomacy.

She condemned Mr Trump calling North Korea’s Kim Jong-un “Rocket man”, adding that she had hoped the President would have called on the nations to work with the United States to try and end the threat posed by the leader, and said “clearly that we will not tolerate any attacks on our friends or ourselves”.

“But you should lead with diplomacy. You should lead with the commitment of trying to avoid conflict however you can,” Ms Clinton added.