(CNN) — Secretary of State Antony Blinken on Wednesday did not promise a meeting with President Joe Biden for the families of Americans held hostage and wrongfully detained abroad, but he sought to assure them that the administration is making every effort to bring their loved ones home, according to a senior State Department official and sources familiar with the video call.

While the families were largely appreciative of the conversation with the top US diplomat, some said they still hoped to meet with the President and others walked away frustrated by what they see as a lack of urgency and concrete action from the administration.

“Stop having meetings with us to check the box and start doing stuff that actually changes things for our families,” said Alexandra Forseth, whose father, Alirio Zambrano, and uncle Jose Luis Zambrano are part of the “CITGO 6” who have been detained in Venezuela since 2017.

Saying she felt “gaslit,” Zambrano said she’d heard the same assurances she’d heard for years about her loved ones’ cases being prioritized but felt that there’s nothing being done.

‘Families were very direct’
In a readout of the call with the families, State Department spokesperson Ned Price said Blinken “relayed to the families that President Biden is aware of each of their loved ones’ cases and is committed to bringing all U.S. nationals held hostage or wrongfully detained home.” The call, which lasted more than an hour, did not get into specific details due to the sheer number of participants — more than 50 — and privacy considerations.

The senior State Department official said that “the families were very direct” on the call, noting that “they have every right to be.”

“Some did ask specific questions about — What is the status of my case? Are you aware of the health condition of a particular individual?” the official said. “We are hearing X, Y and Z from this particular individual, is the embassy engaged on this? Are you raising this with your counterpart? Is the President tracking it?”

The official told CNN that Blinken had conveyed to the families that “a meeting (with Biden) is not required in order for these cases to brought to his attention, and it certainly is not required for us to take certain actions” and “repeatedly assured them” that Biden is fully engaged, because Blinken has had conversations with the President about the cases. The secretary of state also cited that White House scheduling is not in his power and said he would follow up with national security adviser Jake Sullivan, the senior State Department official said.

A second senior State Department official said Blinken also had spoken to Cherelle Griner, the wife of detained WNBA star Brittney Griner, one-on-one on Wednesday. The official did not provide further details about the call, which came after a State Department error had left the couple unable to speak on their anniversary.

‘People are engaged, if not productive’
Neda Sharghi, whose brother Emad Shargi has been unjustly detained in Iran since 2018, told CNN, “We were grateful to have had the call.”

“Our family will continue to ask for a meeting with the President to discuss Emad’s case, as we have been for some time now,” she said, adding that the Bring Our Families Home Campaign — a coalition of family members of unlawful detainees that sent a letter to Biden this week — “will also continue to push for the administration to meet with families and to prioritize the hostages, act with urgency and use all available tools.”

David Whelan, whose brother Paul Whelan has been wrongfully detained in Russia since 2018, said that “to the extent it represents that the State Department, and White House, remain fully engaged in wrongful detention cases, it was a good call.”

“It is useful to hear from him directly about some of the broader issues and concerns facing our loved ones because there is a universality of hurdles, despite the nuances of each case and country involved,” he said. “The amount of time Secretary Blinken spends on these calls and the cases gives me some renewed hope that people are engaged, if not productive.”

Whelan, however, noted that he “didn’t come away with anything that made me think Paul’s case was any closer to being resolved.”

Cristina Vadell, whose father, Tomeu Vadell, has been detained in Venezuela since 2017 as part of the “CITGO 6,” told CNN she was grateful for Blinken’s engagement.

“He’s showing his commitment by taking time with the families, and I hope this commitment to bringing Tomeu and all loved ones home will be translated into more results in the near future,” she said.

However, she also noted that she believes “frustration persists until your loved one is no longer unjustly deprived of freedom.”

“Every day is precious. Why wait another day to make a decision that will free someone?” she said.

Following the call, Forseth added, “Every time we have one of these meetings these officials say, ‘I can’t imagine what it’s like to be in your shoes,’ and ‘I’ll never be able to imagine it,’ and ‘It must be awful.’ “

“Instead of pretending like you can’t imagine, why don’t you try and then ask yourself, do you think you’re doing everything you can, and do you think you’re being honest with yourself about how much people are suffering due to your inaction?'” she said.

‘We should be looking at every available option’
The first senior State Department official told CNN that Blinken had conducted the call — the second by him where all of the families have been invited — because he thought that it was important given the focus on some of these cases in recent weeks, and he wanted to describe the administration’s “intensive efforts to continue to push across the board, no matter what country or what case, to bring them home.”

Blinken did not take the possibility of prisoner swaps off the table during the conversation, according to the first official and sources familiar, but conveyed that such decisions would ultimately have to be made by the President.

“His general approach is we should be looking at every available option, and that’s what he’s directed Roger Carstens and the SPEHA team — don’t sort of withhold any option that you think might be able to secure the release of one American, two Americans, whatever the number is in a particular country,” the first senior State Department official said, using the acronym for the special presidential envoy for hostage affairs.

The official also acknowledged that Blinken has concerns about the “moral hazard” of prisoner swaps and the possibility that they would spur further detentions of Americans abroad.

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