Kayhan wondered how the reformists should be dealt with, saying they "would be a dangerous opposition if they were to win, and set the streets on fire when they lose".
The attacks came as Akbar Hashemi Rafsanjani, an influential former president who backed Mousavi, said the post-election events had caused "bitterness".
But he denied there was a power struggle under way in Iran, according to a report carried by the ISNA news agency on Saturday.
"The election scene was a competition within the system and should not be considered by some as a power struggle or crack in the system," he was quoted as saying.
Rafsanjani has been accused by President Mahmoud Ahmadinejad, both before and after the election, of corruption.
Due to the open support of Khamenei for Ahmadinejad, there had been press reports and speculation that Rafsanjani might start a power struggle against both Ahmadinejad and the religious leadership.
In other news from Tehran, a detained Iranian employee of the British embassy was charged with acting against national security, his lawyer said on Saturday.
Abdolsamad Khorramshi, who is representing Hossein Rassam, said that his client was being held in Evin prison in Tehran, the capital.
"The accusation is that he has been acting against national security," Khorramshi said.
"But what he has done, or how he has done it, is something that will be determined later on, if there are reasons or proof."
Anoushka Marashlian, an independent Middle East analyst, told Al Jazeera that the exact charges against Rassam are unclear.
"He's been seen as acting against the national interest, but they haven't clarified as to what he has been charged with," she said.
"I think [the British government] needs to wait to see what the actual charges are. Is he being charged with treason, which is the accusation that some have levelled against supporters of Mousavi?"
The announcement that a trial was likely came during Friday prayers in Iran.
By then, eight British embassy workers had been arrested, though seven have since been released.
In addition to the embassy workers, Maziar Bahari, a Canadian-Iranian national working for Newsweek magazine, has been accused of acting against national security.
Iran's Fars news agency reported an "interview" with Bahari, in which he said that he had filed "unreal and biased reports from Iran which were driven by greed".
Newsweek repeated a call on Iran to release its correspondent immediately and rejected charges made against him on Wednesday.
The US weekly magazine said that Bahari has been detained in Iran since June 21 without access to a lawyer.
Iranian authorities have also expelled Jon Leyne, a BBC correspondent, and Jason Fowden, a Greek-British journalist for the Washington Times.