The former NYC mayor was attending an annual dinner in Manhattan Saturday, and when it was his time to speak on the terror attacks of Sept. 11, 2001 ... he instead pivoted to a variety of unrelated topics ... including Queen Elizabeth, Gen. Mark Milley and China.

As it relates to Her Royal Highness ... RG was recounting what QE2 said to him and his handling of 9/11 and all the aftermath that followed. Remember, Rudy was head of the city back then -- and has often been commended for how he dealt with Towers coming down.

However, in this re-enactment of the convo, he says they had ... Rudy imitated the Queen, and did it poorly -- putting on a terrible British accent while explaining he turned down a knighthood that she and the Monarchy apparently extended to him. Then, it's on to Andrew.

He says he knows the Duke of York is suspect these days -- and then insists he never hung out with him other than on a couple of occasions where they met briefly. It's ... weird.

In another clip that was captured of his remarks, Giuliani goes off on Gen. Milley -- talking about his stars and how he wants to shove them down his throat ... all while mocking his military decisions with an air base in Afghanistan, getting back to the chaotic withdrawal.