The comments were the first public response by Ayatollah Ali Khamenei, who wields ultimate authority in Iran, to Rouhani's opening to the West in New York last week that was capped by the historic 15-minute telephone conversation with Obama.
"We support the diplomatic initiative of the government and attach importance to its activities in this trip," Khamenei told military commanders and graduating cadets in remarks reported by his website, Khamenei.Ir.
The September 27 telephone conversation, the first diplomatic contact between Iranian and US presidents, broke 34 years of icy relations between Washington and Tehran since its 1979 Islamic revolution.
For Khamenei, who has the final say on all matters of state including foreign policy, suspicions run deep.
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"We are pessimistic towards the Americans and do not put any trust in them. The American government is untrustworthy, supercilious and unreasonable, and breaks its promises," he said.
"Even if the supreme leader is critical, one should not forget that without his permission the diplomatic initiative would not have been put in action in the first place," Leylaz said.
Rouhani's visit to New York for the UN General Assembly came after Khamenei had given the government permission to show "heroic flexibility", raising Western hopes of a breakthrough in long-stalled talks on Iran's controversial nuclear programme.
"Heroic flexibility is very useful and necessary sometimes but with adherence to one main condition," Khamenei told members of the elite Revolutionary Guards on September 17.
There has also been public criticism of the Rouhani-Obama phone conversation from the Guards, whose commander General Mohammad Ali Jafari said on Monday the Iranian president should have waited for US concessions before agreeing to the call.