The British PM admitted last week that he benefited from offshore funds
In a Commons statement as MPs return to Westminster after a 17-day Easter break, the British Prime Minister will announce plans for a new law making it a criminal offence for companies to fail to stop staff aiding tax evasion.
The move was first announced in the March 2015 Budget, when George Osborne said the Government would introduce the measure.
Speaking ahead of his statement, Mr Cameron said: "This Government has done more than any other to take action against corruption in all its forms but we will go further.
"That is why we will legislate this year to hold companies who fail to stop their employees facilitating tax evasion criminally liable."
Some MPs want to challenge Mr Cameron on inheritance tax issues raised by two £100,000 payments made to the Prime Minister by his mother Mary in 2011 after the death of his father, who had already left him £300,000.
Labour leader Jeremy Corbyn said Mr Cameron should now publish his actual tax returns, which he said would reveal more details about his dealing in shares before he became Prime Minister.
"I want to see the papers," said Mr Corbyn.
"We need to know what he's actually returned as a tax return, we need to know why he put this money overseas in the first place and whether he made anything out of it or not before 2010 when he became Prime Minister.
"These are questions that he must answer. I think there is a question for Parliament there, there is a question for Parliamentary standards to question him on this."
The Government says the new law on tax evasion, prompted by the so-called Panama Papers leak, is part of its efforts to clamp down on corruption.
On 12 May, the Prime Minister will host a London Anti-Corruption Summit aimed at stepping up global action to expose, punish and drive out corruption in all walks of life.
The summit will seek to galvanise a global response to tackle corruption, according to the British Government. As well as agreeing a package of actions to tackle corruption across the board, it will deal with issues including corporate secrecy, government transparency, the enforcement of international anti-corruption laws, and the strengthening of international institutions.