President Donald Trump has directly pressured the U.S. Postal Service's chief to double the rates charged to e-commerce giant Amazon and other companies, The Washington Post reported Friday, citing three people familiar with the conversations.

The president has personally pushed the postmaster general, Megan Brennan, to make the move, which could potentially cost Amazon billions of dollars, the Post reported.

Brennan, the first female to hold the role of the Postal Service's chief executive officer, has reportedly pushed back on Trump's demand. The newspaper said Brennan has told Trump that Amazon's shipping arrangements are bound by contracts, and have been beneficial to the Postal Service.

Trump was unswayed by Brennan's arguments, which were made during several meetings starting in 2017 and occurring as recently as four months ago, the Post reported.

Last month, Trump signed an executive order establishing a task force to look at the operations and finances of the USPS and recommend reforms.

In a statement to CNBC, press secretary Sarah Huckabee Sanders said: "We are doing a total look at how the post office is operating. But [we] don't have anything specific for you on that."

Amazon and USPS declined CNBC's requests for comment.

Trump for months has been dinging Amazon and its CEO, Jeff Bezos, who also owns The Washington Post. Amazon, Trump says, has been shirking tax responsibility by failing to collect third-party sales tax at the state level.

Trump tweet

Amazon already collects sales tax on products it sells directly to consumers but has faced challenges from states over its policy of allowing third-party vendors to charge varying levels of sales tax.

States such as South Carolina and Washington have each pushed for state taxes on online items. Amazon has complied with the states' requests so far.

Trump has more than once called for an "internet tax" in thinly veiled threats to Amazon. He tweeted in January that internet retailers would have to start paying sales tax because "it's very unfair what's happening to our retailers all over the country."

Amazon briefly hit a session low of $1,572.10 following the report, but recovered to above $1,574 — less than a percent down on the day. The stock is up more than 30 percent in 2018 and just 4 percent off its all-time high.

The full report on Trump's conversations with Brennan can be found on the Washington Post's website.