President Donald Trump, Microsoft CEO Satya Nadella and Amazon CEO Jeff Bezos attend a meeting of the American Technology Council in the State Dining Room of the White House June 19, 2017 in Washington, DC.

Cassidy's bill doesn't specifically mention China or Amazon, but comes at a time when the president is aggressively going after both.

Those fees are currently set by the U.N.'s Universal Postal Union (UPU), which determines how much each of its member countries pays for the delivery of international mail. In general, the system is set up so that wealthier countries pay more than poorer nations, but in recent years the UPU has provided a huge opening for foreign manufacturers, particularly those in China, to cheaply get products into U.S. online marketplaces like Amazon.

Cassidy, a Republican from Louisiana, proposed the Ending Needless Delivery Subsidies (ENDS) Act, which would force the U.S. Secretary of State to negotiate the end to all foreign subsidies of international postal shipments by Jan. 1, 2021.

Following President Donald Trump's attacks on Amazon in recent weeks and his promise to impose tariffs on goods from China, Senator Bill Cassidy introduced legislation on Tuesday that could make it harder for Chinese manufacturers to compete on U.S. marketplaces.

"The current system costs American jobs at the expense of American taxpayers," Cassidy told CNBC in a statement. "American taxpayers should not be subsidizing Chinese companies mailing items to the U.S., competing with our businesses."

The bill plays into two of Trump's favorite issues: It bolsters Trump's clampdown on what he decries as the uneven trade balance between China and the U.S. and it connects Chinese trade to Amazon, which has opened the floodgates to cheap Chinese products and counterfeits.

On Twitter, Trump has accused Amazon of costing the Postal Service "massive amounts of money for being their Delivery Boy" and criticized a system that makes "Amazon richer and the Post Office dumber and poorer." (The Post Office actually profits from its deal with Amazon, but loses money overall.)

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Trump recently announced tariffs on Chinese steel and aluminum, and last week asked U.S. trade officials to consider another $100 billion in tariffs on Chinese goods. China's commerce ministry has promised to "fight back," and the country has already placed tariffs on U.S. corn and soybeans.

The UPU disparities have been a source of tension for U.S. lawmakers and businesses for several years. In 2015, a Congressional subcommittee held a hearing to discuss the market distortions caused by the inequitable fee structure. Even Amazon supported reforms, with a company vice president telling members of Congress that "the clear losers are American businesses selling to American consumers."

In Tuesday's statement, Cassidy cited a 2015 case study from the USPS, which claimed that low-cost items sent from China are 27 percent cheaper to ship than similar items sent from one U.S. city to another.

However, the problem isn't entirely the result of the UPU. In 2011, In 2011, the USPS started a program with Hongkong Post called ePacket to let businesses in China and Hong Kong send packages to the U.S. at very low rates.