The execution of a 26-year-old Iranian man, Erfan Soltani, accused by the Islamic Republic's government of participating in the protests that swept across the country, has been postponed, according to a human rights group in contact with his family. Soltani was initially set to be executed Wednesday.

Hengaw, an organization that monitors unrest in Iran and has spoken with his family, told CBS News on Wednesday that Soltani's execution "has not been implemented and has been postponed." It was not immediately clear what would happen next, and the ongoing internet blackouts in Iran have hampered Hengaw's ability to provide timely updates on the case. 

The uncertainty over his fate came as President Trump threatened "strong action" against Iran in response to reports of the regime hanging people detained during the protests. Mr. Trump on Wednesday told reporters in the Oval Office that he's heard on "good authority" that the "killing in Iran is stopping" and, "there's no plan for executions or an execution or executions."

The Iranian government "said that he was arrested because of the protest, but we don't know if actually he participated in the protest, because there is absolutely no information about that or evidence," Hengaw representative Awyar Shekhi told CBS News on Tuesday.

Soltani is a clothing seller whose family lives near Iran's capital, Tehran, according to Shekhi, who added that his family has said he was not a political activist but was opposed to the current situation.

An ongoing internet blackout has made it difficult for journalists and rights groups to monitor the protests in Iran or the government's brutal crackdown on them, which sources inside the country say may have resulted in the deaths of some 12,000 people, and potentially many more. More than 2,600 people were detained amid the unrest that began on December 28, according to rights groups.

Now, there are fears that many of those in detention could be executed, despite President Trump's warning on Tuesday to the Iranian regime that if it hangs protesters, the U.S. will "take very strong action."

Soltani was arrested on Jan. 8, Shekhi told CBS News, adding that he had been "deprived from all of his basic rights to contact his family, to have a lawyer."

Four days later, "the family got information that their son has received [a death] sentence, and without declaring what was the charges [or] when the trial took place."

Soltani's family was not told how his planned execution would be carried out, but the most common method in Iran is hanging, Hengaw told CBS News.

Soltani's sister is a lawyer and has been pursuing all available legal avenues to defend her brother, "but the authorities have told [her] there's no case to review and we are not allowing that," Shekhi said.

The activist told CBS News the family was informed they'd be allowed to have a final meeting with Soltani — a procedure normally reserved for the families of those being executed. Hengaw said it had no confirmation that the meeting had taken place, but a source close to the family told the group that some of Soltani's relatives had been heading to the massive Ghezel Hesar prison, in Karaj, late Tuesday night.

"If we want to do a job, we should do it now. If we want to do something, we have to do it quickly," Iran's judiciary chief Gholamhossein Mohseni-Ejei said Wednesday in a video aired on state television, of a discussion he had with other judiciary officials about the handling of detained protesters' cases. "If it becomes late, two months, three months later, it doesn't have the same effect. If we want to do something, we have to do that fast."

Mr. Trump told CBS News' Tony Dokoupil on Tuesday that the U.S. would act if the Iranian regime begins hanging protesters.

When asked to clarify what that action could be, Mr. Trump said:  "Well — let's define it in Venezuela. Let's define it with [ISIS leader] al-Baghdadi. He was wiped out. Let's define it with [Iranian military commander] Soleimani. And let's define it in Iran, where — wiped out their Iran nuclear threat in a period of about 15 minutes once the B-2s got there. And that was a complete obliteration as it turns out, which is what I said initially. Then some questioned it, and they said, 'You know, Trump was right.' So we've been right about everything. We don't want to see what's happening in Iran happen. And, you know, if they want to have protests, that's one thing. When they start killing thousands of people and now you're telling me about hanging - we'll see how that works out for them. It's not gonna work out good."