Both main opposition parties called for the Paymaster General's resignation and insisted his brief personal statement lacked humility, but Tony Blair backed the embattled minister.
The Commons Standards and Privileges Committee demanded the apology after learning that Mr Robinson had used Stenbell, an administrative company that pays salaries to staff working on his New Statesman magazine, to transfer shares to an offshore trust.
The minister also took the opportunity to apologise for failing to register his ownership of an American firm, Roll Center, a breach revealed by The Independent last week. He also told MPs he wished to apologise for the late registration of directorships in two other firms, Agie UK and TransTec plc.
"The House will want to be assured that these shareholdings and directorships were matters of public record. No attempt was made by me at any time to use my position in this House to advance any commercial interest. The oversight concerning registration, for which I apologise, is entirely my responsibility," he said in his one-minute statement.
Ten million shares in TransTec, Mr Robinson's engineering company, were transferred to an offshore trust via Stenbell between February 1996 and October 1997, when his interest in the administrative firm was not registered.
In a report published yesterday, the Standards and Privileges Committee said the transfer represented a significant transaction and the interest should therefore have been registered.
The committee also upheld a complaint that Mr Robinson deleted his directorship of another company, Yamato Lock Inspection Systems, from the register from 31 January 1995 but only resigned from the post on 16 February last year.
The Prime Minister's official spokesman said the apology was sufficient punishment.
David Heathcoat-Amory, Tory spokesman on the Treasury, said Mr Robinson's statement "lacked the necessary humility". He added: "The time for apologies passed long ago. It is time to bring this sorry affair to an end. Nothing less than his resignation as a minister will do."