Sir Keir “absolutely stands by” his language about the previous government’s record, the spokesman told reporters.
Responding on X, Truss said: “I know Keir Starmer won’t repeat his allegations that I crashed the economy because he knows it’s a lie.”
Earlier, Commons leader Lucy Powell told MPs “we won’t cease and desist from telling the truth that they [the Conservatives] crashed the economy”.
Also speaking in the Commons, Chief Secretary to the Treasury Darren Jones said the previous Conservative government had “ruined the lives of people across this country” through their “hubris” and “recklessness”.
It comes as the pound fell to its lowest level in over a year and government borrowing costs have surged to their highest level in 16 years.
Economists have warned these rising costs could force further tax rises or cuts in spending as the government tries to meet its self-imposed rule not to borrow to fund day-to-day spending.
Responding to an urgent question in the Commons, Jones insisted there was “no need for an emergency intervention” in financial markets.
Movements in borrowing costs were being driven by “a wide range of international and domestic factors,” he said.
Tory shadow chancellor Mel Stride said Labour’s tax rises would be “swallowed up by the higher borrowing costs at no benefit to the British people”.
A “cease and desist” letter usually represents a warning that the recipient will face legal action if they continue the allegedly unlawful activity.
In the letter sent to Sir Keir on Thursday, Truss’s lawyers say his statements about their client are “false and misleading”.
“Their publication is not only extremely damaging but also grossly defamatory and indefensible… It would be hard to avoid a conclusion that they were made maliciously,” the letter adds.
Truss’s lawyers say they are seeking “an amicable basis on which you will agree to cease repetition of what is clearly a factually incorrect and defamatory statement about our client.
“This request is made in the context of the basic levels of civility which is due between senior politicians, and we trust that you will respond accordingly.”