Hillary Clinton has publicly mocked US president Donald Trump by pulling out a Russian hat in the middle of a speech at Yale University.

The president’s former Democrat rival brandished the distinctive Ushanka headgear in an apparent dig at Mr Trump over the ongoing investigation into Russian interference in the 2016 presidential election and possible links between his campaign and the Kremlin.

During Sunday's speech, Yale alumna Ms Clinton referred to the university's tradition of wearing outlandish hats on graduation day – explaining she had decided to join in.

“I see, looking out at you, that you are following the tradition of over-the-top hats so I bought a hat too. A Russian hat,” she said, prompting raucous applause from the audience as she raised the furry garment aloft.

In case anyone was in doubt about what she was referring to, the former secretary of State, unexpectedly vanquished by Mr Trump in 2016, added: “If you can't beat them, join them.”

Ms Clinton also used the speech to address her defeat and explained she still had not come to terms with her loss.

"No, I'm not over it. I still think about the 2016 election. I still regret the mistakes I made,” she said. “I still think, though, that understanding what happened in such a weird and wild election in American history will help us defend our democracy in the future."

The former First Lady argued American politics was becoming increasingly polarised and appeared to refer to Mr Trump without mentioning him by name.

“The radicalisation of American politics hasn’t been symmetrical. There are leaders who blatantly incite people with hateful rhetoric,” she said.

Hillary Clinton's life in pictures Show all 10 1 /10 Hillary Clinton's life in pictures Hillary Clinton's life in pictures Hillary Rodham Clinton as a Wellesley College senior Getty Hillary Clinton's life in pictures Bill Clinton and Hillary Rodham in at Wellesley College Getty Hillary Clinton's life in pictures Hillary Rodham Working with the House Committee on Nixon's Impeachment Case Getty Hillary Clinton's life in pictures US Presidential candidate Bill Clinton with wife Hillary and daughter Chelsea at the Democratic National Convention Getty Hillary Clinton's life in pictures Bill and Hillary Clinton at the Inaugural Ball Getty Hillary Clinton's life in pictures Bill and Hillary Clinton with Barbara Bush Getty Hillary Clinton's life in pictures First Lady Hillary Rodham Clinton, President William Jefferson Clinton their daughter Chelsea, at the first state dinner of the Clintons administration Getty Hillary Clinton's life in pictures Hillary Clinton meets with 12 chidren in response to their letter to the President concerning their health problems Getty Hillary Clinton's life in pictures Nelson Mandela jokes with First Lady Hillary Clinton Getty Hillary Clinton's life in pictures Senator Hillary Rodham comforts Maren Sarkarat the conclusion of the Family Memorial Service held at Ground Zero of the WTC Getty