Shares were down by nearly 4% in early trading on Thursday as Mr Trump signalled “concerns” about the tech giant over its tax contributions and the threat it posed to smaller rivals.
That took the company’s market value down by more than $20bn.
Later the shares partly recovered though they were still down by 1%.
It added to a fall of more than 4% – knocking more than $30bn off the valuation – seen the day before, on a report that the President wanted to “go after” the company.
The comments by Mr Trump in a tweet a day later appeared to add weight to the report.
News website Axios said that Mr Trump is obsessed with the retail giant and wants to rein in its power. It follows criticism of Amazon by the President in the past over taxes and jobs.
In his message on Twitter on Thursday, the President said that unlike others, Amazon “pay little or no taxes” to state and local governments, and that they were “putting many thousands of retailers out of business”.
The Axios report on Wednesday said Mr Trump had talked of using antitrust law to “go after” the company because he was worried about small family stores going under.
It also said that he wanted to change Amazon’s tax treatment – an issue he raised publicly last year when he called for an internet tax for online retailers, though Amazon already collects sales tax on items it sells direct to customers.
White House spokeswoman Sarah Sanders said when asked about the report that the President has “said many times before he’s always looking to create a level playing field for all businesses and this is no differerent”.
But she added: “There aren’t any specific policies on the table at this time.”
Amazon founder and chief executive Jeff Bezos also owns the Washington Post, which Mr Trump has criticised as “fake news”.
The newspaper last year won a Pulitzer prize for an investigation into the President’s donations to charities, which found that many of his philanthropic claims were exaggerated.
Amazon is the latest major US tech stock to come under pressure after Facebook acknowledged earlier this month that millions of users’ data had been improperly harvested by consultancy Cambridge Analytica.