Not mentioned in the executive order is the subject for which the USPS has been a topic of Trump's recent public discussion.
In recent weeks, Trump claimed that the service was losing billions due to Amazon. One of Trump's main contentions was that the Jeff Bezos-led retailing juggernaut was ripping off the USPS. Amazon uses the service for much of its last-mile delivery services.
The agency reported a net loss of $2.7 billion in fiscal 2017. The revenue breakdown, however, suggested that shipping and packages were one of the few categories where the USPS made more money year-on-year. The agency, moreover, began losing money in the early 2000s — well before Amazon became the e-commerce giant that it is today.
Though Trump's executive order does not reference Amazon by name, one analyst told CNBC that it was a "shot across the bow" at Jeff Bezos' company.
"Amazon has built its business model on the shoulders of the USPS and Trump is not just talking the talk but now walking the walk with this executive order as a first step, in going after this potential relationship," Daniel Ives, chief strategy officer and head of technology research at GBH Insights, said.
Ives added the jury is still out on what the executive order will result in, but it's clear that Amazon is "in the cross hairs of Trump." While Amazon will continue to use the USPS as a key delivery mechanism, the company's "further investments and infrastructure in last mile delivery might be getting accelerated with Trump on the warpath on this front."
On the other hand, Amazon could simply use the likes of UPS and FedEx for its last-mile delivery, according to Michael Pachter, managing director of equity research at Wedbush Securities.
"USPS will have lower revenues and greater losses," Pachter told CNBC. "The president cannot hurt Amazon by examining the USPS." He explained that while USPS has more competitive rates than UPS and FedEx, they were not dramatically lower.
"If they raise by 10 percent, Amazon may stay with them. However, postal rates are set by an independent commission, and the president's task force has no power to change rates. He is likely not aware of this fact," Pachter said.
Details of Amazon's payments to USPS are not publicly known. Wall Street analysts have estimated it pays USPS roughly half what it would to United Parcel Service or FedEx to deliver a package.
The order's language will likely encourage the task force to see if USPS can charge companies like Amazon more for parcel delivery, a person who previously worked at the Postal Regulatory Commission told Reuters on condition of anonymity.
Amazon declined to comment to Reuters.
The task force will be chaired by Treasury Secretary Steven Mnuchin or his designee, and it will consult with the Postmaster General and the Chairman of the Postal Regulatory Commission, among others, the executive order said.
— CNBC's Jaden Urbi and Reuters contributed to this report.