"This is like a total screw-up," another source close to the EU foreign-policy chief told FP. "This is not the way you treat Mogherini."
Tillerson's office instead offered her a meeting with Brian Hook, the State Department's director of policy planning, sources say. Hook wields significant influence in Tillerson's State Department, but he is several rungs lower on the hierarchy than the secretary of state.
Mogherini declined the offer.
When approached for comment, another EU official, who asked not to be identified, said that Mogherini was never formally refused a call from Tillerson. "We never had to suffer from a denial from the US side for a call with the secretary of state," the official said. "[Mogherini] had several phone conversations with the secretary on different issues."
The official said Mogherini and Hook never spoke. "There is therefore no incident," the official added.
Tillerson's adviser, RC Hammond, didn't deny the incident but told FP that the "the most efficient accommodation under the circumstances was available to her" at the time.
A State Department representative pointed to the regular contact Tillerson and Mogherini have had in the recent past, including their participation in the U.S.-EU leaders meeting during Trump's visit to Brussels on May 25 and several meetings between Mogherini and Vice President Mike Pence in recent months. "Our ongoing, high-level engagement underscores the commitment of the United States to the trans-Atlantic relationship," the representative said.
Officials and former officials briefed on the incident say it could have been a simple scheduling issue - perhaps Mogherini's team didn't give the State Department enough notice. But it's the sort of miscommunication that has become all too common in Tillerson's understaffed State Department. (Tillerson also snubbed the head of the African Union in a scheduling snafu last month.)
Though months into the new administration, the Trump White House hasn't appointed officials to critical middle-management posts that oversee day-to-day relations with Europe, including the assistant secretary of state for Europe, ambassador to NATO, and ambassador to the EU.
That vacuum can cause routine diplomatic contacts like phone calls and debriefings with top allied officials to fall through. "There is a pattern here of not being able to run the logistics of sorting out meetings," the source close to Mogherini said. "They don't have anyone in the administration to pick these things up."
The gaffe came as the Trump administration butts diplomatic heads with Europe over issues such as trade and defense spending. "This administration has a very skeptical view about multilateral institutions like the EU," said Anthony Gardner, who until January was US ambassador to the EU. He cited Trump's coterie of euroskeptic advisors and friends, including strategist Stephen Bannon and Brexit architect Nigel Farage.
But given the turmoil in the administration, erratic messaging, and unfilled administration vacancies, European officials aren't even sure what explains these types of snubs.
"Europeans are wondering, surely this isn't a direct hit against us, is it? Does it highlight their understaffing, their incompetence ... or is it intentional?" one former senior US official familiar with the incident told FP.
Former officials say missteps are common in the early months of a new administration - as are tensions between a new administration and its EU allies (even under former President Barack Obama). But Trump has taken a decidedly combative tone toward the EU, such as using Twitter to spark a public spat over trade with Germany, the EU's most influential member. German centre-left chancellor candidate Martin Schulz lashed back, calling Trump on Tuesday "the destroyer of all Western values".
Last week, Trump undertook a trip to Europe rife with tensions, including an awkward and widely criticized visit to NATO and a meeting with top EU officials in which European Council President Donald Tusk took the unusual step of publicly conceding he couldn't find common ground with Trump on Russia.
Current and former officials who spoke to FP say that regardless of how the Trump administration views the EU, Mogherini could be a valuable ally in Brussels if it treats her as an equal. "I think she is one of the most effective members of the [EU Commission] team," Gardner said.
Many officials laud Mogherini for her accomplishments on issues such as the Iran deal and penning the EU's first-ever global strategy.
"I saw her a lot up-close quite a bit. She was always prepared. She certainly enjoyed the confidence and respect of Secretary [John] Kerry," Gardner told FP, referring to the former secretary of state. Kerry worked hand-in-hand with Mogherini on issues such as the Iran deal, climate change, and terrorism.
Given the array of threats the EU and United States face, it's an important relationship. "On almost every threat, closer U.S.-EU cooperation would be helpful," said Jeremy Shapiro, research director at the European Council on Foreign Relations. He said it was difficult to find a coherent EU foreign policy given the 28-country bloc's varying national priorities, meaning other European leaders may wield more influence than Mogherini.
But experts say keeping regular contact with the EU is a low-cost, high-payoff way for the United States to support the EU's foreign policy. It's work that may not make the top headlines but is critical to trans-Atlantic security, such as counterterrorism work in Africa and stabilizing the politically fragile Balkans.
"The United States and Europe have so many common policy topics that they coordinate on, consult on, and work together on," said Constanze Stelzenmüller of the Brookings Institution.
"This is not trivial. It's not diplomatic flag-waving," she said. "This is getting down to business and solving problems."