Sky News understands Mr Johnson had a “constructive” conversation with Richard Ratcliffe at 9.30am on Sunday.
The two agreed to meet in person over the next few weeks.
Their call came 20 minutes before Environment Secretary Michael Gove sparked a further row.
Asked what charity administrator Nazanin Zaghari-Ratcliffe was doing when she was arrested in Tehran in 2016, Mr Gove said: “I don’t know.”
It follows Mr Johnson’s claim that the 38-year-old mother was “training journalists” – which could add five years to her current sentence.
Mrs Zaghari-Ratcliffe’s family and employer say she was on holiday visiting family when she was arrested with her daughter at an airport in Tehran.
After Mr Gove’s remark on the BBC’s Andrew Marr Show, he was told her husband’s explanation.
“In that case I take exactly her husband’s assurance in that regard,” he said.
“Her husband said she was there on holiday, and her husband is the person who should know.”
Labour’s Chris Bryant said the comments were proof of an “incompetent” Government.
He told Sky News: “Boris got into trouble because he hadn’t bothered to check details before he went to the Foreign Affairs select committee.
“Michael Gove must have known he would be asked that question and yet answered in that way. It’s a Government of incompetence”.
Mr Gove also branded the Iranians “extremists” and accused them of “harming the human rights of someone whose plight moves us all”.
Defending his Cabinet colleague who is facing calls to resign, he also criticised those trying to “blame politicians in a democracy who are trying to do the right thing”.
“We play their game if we do anything other show than solidarity in the face of their abuse of human rights,” he said.
Labour leader Jeremy Corbyn has also launched a furious attack on Mr Johnson, calling on him to quit for “putting our citizens at risk”.
He said the “embarrassing” behaviour over Mrs Zaghari-Ratcliffe case, coupled with the Foreign Secretary’s “colonial throwback” attitude meant he should resign.