Alexander Temerko, a Ukraine-born businessman who has given more than £1m to the Conservatives, said "corrections" were needed, while others called for an inquiry into the rules around political donations.
Chris Bryant, the chair of the Commons Standards Committee, called for a system that had "full, not cloudy or murky transparency".
The prime minister warned MPs yesterday that they would have to "justify" all the money they accepted to their constituents and as Downing Street said politicians "should be in no doubt that the public will pay close attention".
The reform calls came after it emerged that some businesses have donated significant amounts to individual MPs despite having no employees or operating from apparently empty offices, according to an investigation by Sky News and the Tortoise website.
The government of Qatar was the fourth-biggest donor, with its Ministry of Foreign Affairs giving nearly £250,000 worth of benefits in kind, Sky reported. Asked if it was right that "companies that don't seem to exist" could donate to MPs, Mr Sunak said: "I think transparency is really important for the healthy functioning of democracy."
He also warned it was important that MPs keep to strict rules on outside incomes after it was revealed that Theresa May was one of the highest earners in parliament, alongside shadow foreign secretary David Lammy, despite Labour leader Sir Keir Starmer's opposition to MPs having second jobs.
Asked about companies that appear on the register, No 10 said that every MP "should be in no doubt that the public will pay close attention to that and they will obviously need to justify that to their constituents".
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