The hardline Kayhan newspaper accused the reformist Khatami of tarnishing the Islamic republic's reputation by implying it was carrying out "sabotage" work in other countries through insurgent groups.
In his speech, Khatami referred to the ambition of Iran's revolutionary leader Ayatollah Ruhollah Khomeini to export the 1979 Islamic revolution around the world, but expressed fear this wish was being distorted.
"What did the imam (Khomeini) mean by exporting the revolution?" he asked in the speech Friday to university students in the northern province of Gilan, according to the Kargozaran newspaper.
"Did he mean that we take up arms, that we blow up places in other nations and we create groups to carry out sabotage in other countries? The imam was vehemently against this and was confronting it," he added.
His speech has been seen by some observers as accusing the Iranian authorities of encouraging militants to destabilize the Middle East, in particular Iraq and Lebanon.
The controversy comes at a particularly sensitive moment.
The United States has stepped up accusations that Shiite-majority Iran is arming and training Shiite militias in Iraq and is working to destabilise Lebanon through the Shiite militant group Hezbollah.
A high-ranking Iraqi parliamentary delegation visited Iran last week in an apparent bid to end clashes between the security forces and Shiite militiamen loyal to anti-US cleric Moqtada al-Sadr.
Sadr is believed to be studying in the Iranian clerical centre of Qom but Tehran has always refused to confirm his presence.
"It is obvious that Mr Khatami must answer for his anti-patriotic comments and explain why he has taken such a stance," said Kayhan, whose editor-in-chief is appointed by supreme leader Ayatollah Ali Khamenei.
"Its only consequence has been to tarnish the shining reputation of the Islamic republic and its system, and confirm the baseless accusations of the arrogant powers," Kayhan said.
The government daily Iran also expressed concern about the speech. "US media used Khatami's comments as a pretext for bringing up the US claims against Iran," it said.
A hardline MP also hit out at the former president "whose comments have been exploited by the enemy," the hardline website Rajanews reported.
"Mr Khatami has not differentiated between the criminal acts of the Taliban and the martyr operations of Lebanon's Hezbollah or Muslim fighters in Palestine," Mehdi Kouchakzadeh was quoted as saying.
"Mr Khatami has to make it clear whether using fervent martyrdom-seeking young men to combat occupiers is an ugly and violent act or a fully human and admirable one?" demanded the MP.
Conservative website Tabnak also accused Saudi-funded news channel Al-Arabiya of distorting the speech by representing it as an accusation that Iran "exports violence and crisis to other nations".
Iran vehemently denies the charges it is destabilising Lebanon and Iraq saying that foreign intervention in both nations are the root cause of their crises.
