In other exchanges, he implied that he had people on the ground in Ukraine monitoring the then-ambassador, and gave supposed updates on her activity.

"She under heavy protection outside Kiev," he wrote, also on March 23.

"They are moving her tomorrow," Hyde wrote two days later, again apparently referring to Yovanovitch. "The guys over they (sic) asked me what I would like to do and what is in it for them."

A few hours later, Hyde wrote, "She's talked to three people. Her phone is off. Computer is off." The updates kept coming: "She's next to the embassy," "Not in the embassy", "Private security. Been there since Thursday," and "They will let me know when she's on the move."

Parnas responded with brief replies, such as "Interesting" and "Perfect."

On March 26, 2019, Hyde wrote: "Update she will not be moved special security unit upgraded force on the compound people are already aware of the situation my contacts are asking what is the next step because they cannot keep going to check people will start to ask questions."

Yovanovitch testified in the House impeachment inquiry last year. She described how alarmed she felt as Giuliani and others tried to undermine her standing in Kyiv. She said that in April, as State Department officials told her to fly quickly to Washington for consultations, one official spoke of "great concern” for her safety.

She also talked about her astonishment at learning that, in a July 25 call with Ukraine’s president, Trump had derided her as “bad news” and said she’s “going to go through some things.”

Lev Parnas, an associate of President Donald Trump's lawyer Rudy Giuliani. | Stephanie Keith/Getty Images

In a statement, Yovanovitch's lawyer, Lawrence Robbins, called the latest news "disturbing." “We trust that the appropriate authorities will conduct an investigation to determine what happened,” he said. He declined to comment further.

It was difficult to tell how real or serious Hyde's apparent claims of monitoring Yovanovitch were. In a Facebook post Tuesday, he slammed House investigators, writing: "I was never in Kiev. For them to take some texts my buddy’s and I wrote back to some dweeb we were playing with that we met a few times while we had a few drinks is definitely laughable."

In a television interview with Eric Bolling aired on Wednesday evening, Hyde said he never surveilled Yovanovitch and that he was “joking around” in his messages with Parnas.

Hyde styles himself as an ardent Trump supporter and has posted pictures of himself with the president online. White House spokespersons did not reply to a request for comment on the president's relationship with Hyde.

It's not clear whether the systems in place for protecting U.S. diplomats from on- and offline surveillance would have discovered the monitoring of Yovanovitch — if it indeed incurred.

A former U.S. ambassador said the State Department needs more funding to improve its cybersecurity, but that its physical security protocols are "very good."

"All of that said, they’re not necessarily going to be looking for threats from a guy running for Congress in Connecticut," the former ambassador said. "To get info on a U.S. person, especially one who is friends with the president, would require jumping through a lot of legal hoops."

Diplomatic security "would always tell you about a potential threat, but this was an American, so they probably didn’t even know about it," the former ambassador said.

Former U.S. Ambassador to Russia Michael McFaul agreed. “What’s so odd about this is that it’s allegedly an American who’s doing the surveilling, so who do you go to?” he said. “Hyde also made it sound like somebody was on the inside helping them. As you would imagine, certainly in Russia, we were always wary of the possibility that somebody on the embassy staff could be compromised.”

A former senior State Department security official agreed that a threat coming from a fellow U.S. citizen might be more challenging to spot and that there would be additional legal hurdles to investigate it. But the former security official also said some of Hyde's claims appear puffed up, in part because it doesn't take all that much to track the location of a U.S. ambassador overseas.

U.S. ambassadors are generally fairly open about their whereabouts in their host country. They travel in armored vehicles and are often impossible to miss, the former security official said.

There's an expectation that ambassadors will face physical and electronic surveillance, including from other countries that might be hostile to the United States, the former security official said. In Ukraine, the Russians would be especially keen on tracking the U.S. ambassador given America's support for Kyiv in its territorial war with Moscow.

Ambassadors are trained on how to deal with such surveillance. For instance, they are supposed to be careful not to use personal devices to discuss classified information, or even to talk about sensitive issues in front of their security escorts, who are likely local residents.

State Department official devices have safeguards to prevent hacking from anywhere, including the United States.

It's not clear if Hyde had Yovanovitch's cell phone number, but he could have simply called it to figure out that it was turned off. Less clear was how he would know that her computer was off.

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The former senior security official said although the notion of an ambassador being under surveillance wouldn't be surprising, a key question is: "Is there an actual physical threat against her? Are there people wanting to kidnap her or kill her? Some kind of attack on her?"

The former security official said what needs to happen now, if it hasn't already, is that people involved with Yovanovitch's security details receive additional vetting.

It's possible some have loose lips, the former official said: "I don’t think any of them would breach their duty in terms of protecting her. But would they talk to their brother-in-law, their brother?"

The latest revelations further rattled U.S. diplomats who have already been deeply frustrated with Pompeo over his handling of Yovanovitch's situation and his unwillingness to publicly defend her.

State Department staffers contacted by POLITICO used terms like "crazy," "appalling" and "Keystone Cops" in reacting to the news.

"Pompeo should be out there immediately explaining how this happened on his watch," one staffer said. "It's really shocking even in this administration."