Trump, the Republican nominee for president, started the latest exchange Saturday morning when he again referred to the Massachusetts senator as "Pocahontas," a reference to her claimed Native American heritage.
"Pocahontas wanted V.P. slot so badly but wasn't chosen because she has done nothing in the Senate. Also, Crooked Hillary hates her," he tweeted.
Warren, arguably the Democrats' most vocal Trump opponent, dismissed the real estate mogul's claim that she was disappointed she wasn't chosen.
"I'm right where I want to be, @realDonaldTrump: Calling you out & holding you responsible for your reckless vision for America," she tweeted.
She didn't address Trump's suggestion that Clinton "hates her."
Warren, a favorite among progressives, was considered a possible but unlikely choice for the VP slot. So far, she has notably abstained from weighing in on Kaine, despite several other Clinton VP contenders -- including New Jersey Sen. Cory Booker, Labor Secretary Tom Perez and Agriculture Secretary Tom Vilsack -- praising her choice.
A message left with Warren's office was not immediately returned Saturday.
Warren and Trump have regularly engaged in social media skirmishes for months. Hours after Trump emerged as the presumptive Republican nominee in May, Warren tweeted
that Trump "built his campaign on racism, sexism, and xenophobia."
In June, she called the Republican nominee a "thin-skinned, racist bully"
; in turn, Trump said the Massachusetts senator was "very racist"
for claiming she had Native American heritage while teaching at Harvard University in the 1990s.
Last week, Warren trained her Twitter sights
on Trump's own running mate, Indiana Gov. Mike Pence, calling the two Republicans "small, insecure, weak men."