David Cameron has suffered a "significant erosion of trust" because he has not been straight from the start over his finanical affairs, according to Labour, Sky News reported.
The Prime Minister's admission he had profited from shares in an offshore fund operated by his late father had to be "dragged out of him", shadow chancellor John McDonnell said.
However, despite his criticism, Mr McDonnell said it was not a resignation issue "at the moment".
One Labour MP, John Mann, a high-profile campaigner for more tax transparency, has reported Mr Cameron to the parliamentary standards watchdog.
Lib Dem leader Tim Farron said Mr Cameron's actions were "morally murky" and also indicated the episode would damage the campaign to stay part of the EU in the upcoming referendum.
The Prime Minister, who has insisted he has does not have "anything to hide", has come under fire over why it took him so long to make his position clear.
The Tory leader has also been accused of hypocrisy because of his previous tough-talking on tax avoidance.