The Islamic republic has yet to announce who will travel to South Africa for Tuesday’s memorial service and next Sunday’s funeral for the late president and Nobel laureate.
Hardline newspaper Kayhan warned in an editorial that if Mr Rouhani attends it could bring him face to face with Mr Obama, “head of the Great Satan government”.
“Some domestic and foreign media outlets are using the funeral ceremony as a pretext to push Rouhani towards a meeting with the head of the Great Satan government,” Kayhan said.
Mr Rouhani, a moderate, defeated a pool of conservatives in a June presidential election after vowing to engage with the West.
Since then there has been a thaw in ties between Iran and world powers.
The call was the first contact between leaders of the two nations since diplomatic ties were severed more than three decades ago over the hostage-taking at the US embassy in Tehran.
The Kayhan editorial, headlined “Satan lays a trap, this time in Johannesburg”, recalled comments by supreme leader Ayatollah Ali Khamenei after Mr Rouhani’s September trip to New York.
“Some of what happened in the New York trip was not appropriate,” Ayatollah Khamenei said at the time, without elaborating.
Iranian hardliners and conservatives took that as indicating the supreme leader was unhappy the telephone chat had taken place.
Since that conversation, Iran has struck a landmark nuclear deal with six world powers including the United States in another sign of a thawing of ties.
The interim agreement reached last month following a decade of gridlock would freeze parts of Iran’s controversial nuclear program while easing some of the crippling international sanctions against it.
It is not clear if Mr Rouhani will attend services for Mandela, but he sent a message of condolences following the death of the iconic South African.
Foreign Minister Mohammad Javad Zarif has also tweeted a message saying: “We in Iran join the people of South Africa in mourning the death of Nelson Mandela, who inspired humanity with his courage&compassion.”
Mandela, who died late on Thursday at the age of 95, had visited Iran in 1992 and again in 1999.
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