A senior Iranian official has made the astonishing claim that Republican members of Congress asked the Iranian government to delay the release of Pastor Saeed Abedini and three other American hostages until the 2016 elections.

Iran's Tasnim News Agency reports on an address to a rally held in the central city of Yazd to mark the 37th anniversary of the 1979 Islamic Revolution. The Secretary of Iran's Supreme National Security Council, Ali Shamkhani, told the gathering: "In the course of the talks for exchanging prisoners, the Republican rivals of the current US administration who claim to be humanitarians and advocates of human rights sent a message telling us not to release these people [American prisoners] and continue this process [of talks] until the eve of US presidential elections."

"However, we acted upon our independent resolve and moved the process forward," he said.

Shamkhani said Iran's move to exchange prisoners was based on the country's "humanitarian approach".

Iran released the prisoners – Amir Mirzaee Hekmati, Jason Rezaian, Saeed Abedini, and Nosratollah Khosravi – on January 16. Abedini, a convert from Islam, had been in prison since 2012 accused of undermining national security by holding Christian religious gatherings in homes. His cause was taken up by Republican evangelicals including Franklin Graham, who accused the Obama administration of not doing enough to get him out. It was later revealed that his marriage was under strain and his wife Naghmeh has filed for a legal separation but has said she wants to be reconciled to him and for their marriage to work.

After he was released, Republican candidates expressed thanksgiving for his freedom but took the opportunity to criticise Obama for giving too much away in return.

Donald Trump said: "I am happy they are coming back, but it is a disgrace they have been there this long, a total disgrace." Ted Cruz, who had appeared alongside Naghmeh Abedini, said the release "reflects a pattern we have seen in the Obama administration over and over again of negotiating with terrorists, and making deals and trades that endanger US safety and security".

Marco Rubio said the hostages "should never have been there" and that Iran takes people hostage in order to take concessions. "And the fact that they can get away with it in this administration...has created an incentive for more governments to do this around the world."

The claims by Shamkhani that the Republicans deliberately attempted to prolong the ordeal of the hostages for their own electoral advantage will be dismissed by the candidates, who could argue that Iran is attempting to brief against them for its own purposes. The leaders in the Republican race have said they will revisit the nuclear deal that is seen as the major foreign policy achievement of President Obama's administration.