She said journalists in a democratic society such as New Zealand should be free to do their job without interference and intimidation from politicians.
Alexander said it was an alarming development that Peters was seeking payment of "general damages" from the journalists for compensation for allegedly breaching his privacy.
"The significant public interest in an MP being overpaid superannuation overrode any entitlement to privacy.
"The journalists facing legal action, and others covering the story, were simply doing their job and, in fact, the issue demanded scrutiny given Mr Peters was seeking re-election to Parliament. Voters were entitled to know what had happened.
"Mr Peters could have cleared the matter up by explaining at the outset how the seven-year overpayment occurred, how much he had been overpaid and how much he paid back. Instead, those details remain unknown.
"The Media Freedom Committee believes Mr Peters should drop the legal action against the two journalists," Alexander said.
Today, the Herald reported that National's campaign manager and MP, Steven Joyce, publicly denied leaking details of Peters' superannuation overpayment and says, if anyone in National had approached him about it, he would have told them not to do it.
The Media Freedom Committee represents the country's major news and current affairs organisations including Fairfax/Stuff, NZME, the Newspaper Publishers' Association, TVNZ, MediaWorks and RNZ.