"The turbulent state of the region and the world and the international adventurism of oppressors and their vassals have confronted the Islamic Iran with conditions more complicated than before," said a message from Khamenei, read to a packed parliament chamber.
Khamenei, who has the final say on all matters in the country, repeated his familiar call for loyalty to the principles of the 1979 revolution and resistance against Western infiltration.
"Arrogance" was a term first used by the Islamic republic's founder Ayatollah Ruhollah Khomeini to describe Western powers, especially the United States.
The 290-member parliament was inaugurated in the presence of 265 members, with three seats vacant after votes for two MPs were nullified by Iran's constitutional oversight body, the Guardian Council, and a third member died in a car accident.
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Elections for the key position of house speaker and the presiding board are expected tomorrow or Monday.
According to an AFP count, no single party won an overall majority in elections that saw Rouhani make huge gains.
Reformists took 133 of the 290 seats, short of a majority but ahead of conservatives, who took 125 seats.
The role of the independent members will be critical in the balance of parliament's partisan powers.
Incumbent conservative speaker Ali Larijani and reformist Mohammad Reza Aref are the top candidates standing for the position.
Iranian media say Larijani, who supported last year's nuclear agreement with major powers, seems to have the upper hand.
Today's opening session comes less than a year after long negotiations between Rouhani's government and world powers culminated in a nuclear agreement that took effect in January and saw economic sanctions eased on Tehran.