* Shares of Amazon near flat amid volatile trading
* President renews criticism over retailer's use of USPS
* Trump says Amazon does not pay fair shipping rate (Adds Trump comments to reporters, updates share price)
WASHINGTON, April 3 (Reuters) - Shares of Amazon.com Inc pared earlier gains on Tuesday after U.S. President Donald Trump repeated his unsubstantiated claim that deliveries for the world's biggest online retailer cost the U.S. Postal Service money and threatened to raise rates.
Citing an unnamed report, Trump told reporters at the White House the company is not paying the USPS a fair rate, costing U.S. taxpayers billions of dollars and forcing other retailers out of business.
It was the latest salvo in a string of attacks in recent days as Trump stepped up his criticism of Amazon and its founder and Chief Executive Jeff Bezos, who privately owns The Washington Post.
Amazon shares were down about 0.3 percent in early afternoon trade on the Nasdaq after trading up about 1.8 percent on Tuesday morning before Trump's latest Amazon-related tweet, making another day of volatility after its shares fell more than 5 percent a day earlier.
Trump attacked the company over its shipping on Monday after criticizing it last week over taxes.
On Tuesday, he said the federal government was subsidizing deliveries for Amazon and the company would need to pay more.
"The post office is losing billions of dollars ... because it delivers packages for Amazon at a very low rate," Trump told reporters. "If you look at the cost that we're subsidizing, we're giving a subsidy to Amazon."
Trump offered no specific details about the report he cited to back up his criticisms or how he planned to charge the company more through USPS.
Amazon also ships packages through other providers such as FedEx Corp and United Parcel Service Inc as well as its own experimental shipping service. Representatives of Amazon and USPS had no comment on Trump's tweet on Tuesday, and could not be immediately reached regarding his latest comments to reporters.
Reporting by Steve Holland Additional reporting by Makini Brice and Lisa Lambert Writing by Susan Heavey Editing by Bill Rigby and Chris Reese