The issue burst into public view with a report in Iran of a deal for the Islamic Republic to release USA and British prisoners in exchange for Tehran receiving billions of dollars.
Speaking earlier Sunday before the Iranian report emerged, British Foreign Secretary Dominic Raab said Zaghari-Ratcliffe was being held "unlawfully" and "being treated in the most abusive" way.
Even after an initial American denial, an anchorwoman on Iranian state TV still repeated the announcement.
The state TV report had said the Biden administration had agreed to release four Iranian prisoners being held in the U.S. in exchange for four American "spies, '" per Reuters.
Denying claims of the Iranian government, Sadiq Tulip, member of Parliament for Zaghari-Ratcliffe's constituency, Hampstead and Kilburn tweeted, "I am aware there are news reports circulating about the debt being paid to #FreeNazanin".
"The news of the agreement for the release of American prisoners [in Iran] is not confirmed", Majid Takht Ravanchi was quoted as saying by the Young Journalists' Club, which is affiliated with state media.
"We have not yet discussed with her what two more years without mummy means", he said in an article published Saturday on the website Declassified UK.
US officials regularly raise the issue of detained Americans with Iran, Klain said.
"We're working very hard to get them released", Mr Klain said.
Ron Klain, White House chief of staff, also denied the report.
Nazanin Zaghari-Ratcliffe to be released from prison when UK pays £400m fee, Iranian state TV reports
"I think it amounts to torture the way she's being treated, and there is a very clear, unequivocal obligation on the Iranians to release her", he told BBC television.
Despite the American denials, there have been signs that a deal on prisoners may be in the works based on Iranian officials' remarks in recent weeks.
Officials in Washington did not immediately respond to requests for comment.
State TV also reported that Nazanin Zaghari-Ratcliffe, a British-Iranian dual national who has been held in the country since 2016, was being freed after "payment of military debt".
But the British Foreign Office said only that talks over the debt were ongoing after four decades.
Iran will free a number of prisoners with Western ties - including British-Iranian woman Nazanin Zaghari-Ratcliffe - in exchange for billions of pounds from the U.S. and the United Kingdom, according to state television.
That came after she completed a five-year sentence in the Islamic Republic after being convicted of plotting the overthrow of Iran's government, a charge that she, her supporters and rights groups deny.
Her husband, Richard Ratcliffe, said the family had not been updated but welcomed the signals from Tehran over the long-running dispute as "a good sign".
"We recognise the IMS debt should be repaid and we're looking at arrangements for securing that", Raab told Times Radio. "Of course we probably wouldn't, but my instinct is to be sceptical at present".
Australia bans direct passenger flights from India till May 15
On Thursday 3,498 people died in India from Covid-19, at the end of a horror week where daily deaths averaged over 3,000. More than 9000 Australians in India are registered as wanting to return, including 650 people registered as vulnerable.