The claim relates to transactions, originated between 1995 and 2005 and terminated in December 2011 and January 2012, which the Lazio regional court's investigative office argues were unfairly weighted in the bank's favour.
Controversy is swelling in Italy over the Treasury's use of derivatives, which were its weapon of choice to insure its 2.2 trillion euros public debt - the second highest in the euro zone relative to economic output - against rising interest rates after the 2008 financial crisis.
Opposition parties are calling for the publication of all the contracts, including those with Morgan Stanley which cost Italy 3 billion euros to close, but the Treasury has refused.
Morgan Stanley said in a securities filing last year the prosecutor had proposed it pay 2.9 billion euros to settle the transactions. A spokesman for the bank said the claim was groundless.
Prosecutor Donata Cabras said on Friday that Morgan Stanley had a "dominant" role in its dealings with the Treasury, which in turn tended to "submit to some of the bank's choices".
Cabras's deputy Massimiliano Minerva said at a conference in Rome that Treasury executives should pay 1.2 billion euros in damages relating to the derivatives.
A judicial source said the executives in question are head of debt management Maria Cannata, Treasury director general Vincenzo La Via, and former economy ministers Domenico Siniscalco and Vittorio Grilli.
The Treasury declined to comment. A spokesman for Morgan Stanley, where Siniscalco now works, declined to comment on behalf of the former minister and the bank. A spokeswoman for Grilli also declined to comment.
The court's prosecutors are still investigating the case and, once their probe is wrapped up, a judge will have to rule on their requests.
Cabras said the derivatives were too risky for a state to take on, and were not suited to reducing Italy's public debt.
The derivatives contracts the state enters into are interest-rate swaps, which the Treasury says help protect against a sudden interest rate rise, and therefore does not threaten the stability of public finances.
However, rates are very low at the moment putting the state on the wrong side of the swap. The negative impact on public finances broadly is that the debt increased by 23.5 billion euros, according to a document the Treasury submitted to parliament on Thursday.
The opposition 5-Star Movement, which is riding high in opinion polls, has seized on the case against Morgan Stanley and the Treasury officials.
"Derivatives are the symbol of a criminal financial system that has stolen sovereignty from the people and given it to the big investment banks and the politicians that manipulate them," it wrote on its blog this week.
($1 = 0.9397 euros)
(Writing by Isla Binnie)
By Giuseppe Fonte and Isla Binnie