Williams claimed that Trump was "well past the last exit to relevance" after his previous Twitter outburst following Barack Obama's re-election to the presidency.
Trump responded: "@bwilliams knows that I think his newscast has become totally boring so he took a shot at me last night.
"The only thing more boring than @bwilliams newscast is his show Rock Centre which is totally dying in the ratings-a disaster! @bwilliams--wouldn't you love to have my ratings?"
He continued: "I hope NBC isn't paying you too much-look at what's happening to nightly news.
"If I'm "well past the last exit to relevance" how come you spent so much time reading my tweets last night?"
© Charles Sykes/AP/Press Association Images
© PA Images / Charles Sykes/AP
Trump added: "Brian--Thanks dummy--I picked up 70,000 twitter followers yesterday alone. Cable News just passed you in the ratings.
"Brian Williams was never a smart guy but always passes himself off as such. People will learn the truth!"
In relation to Obama's victory, Trump said: "This was the Republicans election to win. @MittRomney is a good man but he just never connected with the people.
"The voting booth process was a total disaster - it could and should be much better and more efficient - tremendous room for error!"
