Vida Mehran Nia told AFP she had been informed by her husband's lawyer that Iranian authorities had decided to delay the execution for “some days”.
According to information gathered by human rights group Amnesty International, Djalali was scheduled to be moved on Tuesday afternoon to a prison in the Iranian city of Karaj where the execution was to be carried out, but his wife said he had not yet been transferred.
Mehran Nia told AFP she believed the postponement was related to “political issues” in Iran, and even if it was a “good sign” she was unsure what it meant for her husband's chances.
“I don't know honestly, but at least we have some hope,” said Mehran Nia.
Djalali, formerly based in Stockholm where he worked at the Karolinska Institute, a medical university, was arrested during a visit to Iran in April 2016. He was subsequently found guilty of passing information about two Iranian nuclear scientists to Israel's Mossad intelligence agency that led to their assassinations.
Djalali has claimed he is being punished for refusing to spy for Iran while working in Europe and his death sentence has been widely condemned by rights groups and by UN rights experts.
While imprisoned he was granted Swedish citizenship in February 2018, only months after his death sentence was confirmed by Iran's Supreme Court.
The case strained relations between Sweden and Iran after Swedish foreign minister Ann Linde urged Tehran to call off the execution on Twitter last week, writing that she had spoken to her Iranian counterpart Mohammad Javad Zarif about the case.
“Sweden denounces the death penalty and is working so that the sentence against Djalali is not carried out,” Linde wrote.
Linde's comments were denounced by Iran the following day, with foreign ministry spokesman Saeed Khatibzadeh saying that “all interference in the issuance or carrying out of judicial decisions is rejected as unacceptable”.
Sweden's foreign ministry declined to comment Thursday on any updates in the case.