Donald Trump's commerce secretary is shown to have a stake in a firm dealing with Russians sanctioned by the US.
The leak, dubbed the Paradise Papers, contains 13.4m documents, mostly from one leading firm in offshore finance.
The Paradise Papers also show that about £10m ($13m) of the Queen's private money was invested offshore.
It was put into funds in the Cayman Islands and Bermuda by the Duchy of Lancaster, which provides the Queen with an income and handles investments for her £500m private estate.
There is nothing illegal in the investments and no suggestion that the Queen is avoiding tax, but questions may be asked about whether the monarch should be investing offshore.
As with last year's Panama Papers leak, the documents were obtained by the German newspaper Süddeutsche Zeitung, which called in the International Consortium of Investigative Journalists (ICIJ) to oversee the investigation. The UK Guardian and BBC Panorama are also among the organisations investigating the documents.
Sunday's revelations form only a small part of a week of disclosures that will expose the tax and financial affairs of some of the hundreds of people and companies named in the data, some with strong UK connections.
Many of the stories focus on how politicians, multinationals, celebrities and high-net-worth individuals use complex structures of trusts, foundations and shell companies to protect their cash from tax officials or hide their dealings behind a veil of secrecy.