Kris Engskov, the company's UK managing director, demanded urgent talks at Downing Street after Prime Minister David Cameron took a thinly veiled swipe at the coffee giant, the Sunday Telegraph said.
Starbucks has not been singled out for criticism over tax, a senior Tory insisted after the firm reportedly threatened to abandon UK investment plans over the politicisation of the issue.
In a speech at the World Economic Forum in Davos promising to lead global action against tax avoidance, Mr Cameron said it was time for businesses to "wake up and smell the coffee" about public anger.
Starbucks has been one of the highest profile targets of protests about "aggressive" tax avoidance after it emerged it paid no corporation tax in the last three years and only £8.6 million in 14 years of trading in Britain
While the firm has since changed its tax arrangements so it will pay around £10 million in corporation tax this year, the revelations sparked a customer boycott and political accusations of immoral behaviour.
Mr Cameron has faced a business backlash over his campaign, with Goldman Sachs chief executive Lloyd Blankfein saying the criticism risked "criminalising every right-thinking person who organises his or her affairs in a sensible way".
And Mr Engskov was reported to have used the meeting to threaten to put on hold a planned £100 million investment in new UK branches of the coffee chain, which employs 9,000 staff in the UK.
A company source was quoted by the newspaper as saying Mr Cameron was "singling the business out for cheap shots".
"A company that, it should not be forgotten, has pledged to pay tax now and into the future," they added.
Asked about the disagreement, Conservative Party chairman Grant Shapps told the Murnaghan programme on Sky News: "I don't think we would ever single out a single company but I do think companies in this country need to pay their way."