Iraq launched a major air offensive against Iran's cities today in what officials described as a "very big and very serious" push to force Iran into peace talks.

Iran retaliated with shelling of the Baghdad suburb of Mandali and an air strike against the southern Iraqi city of Al Amarah, according to news agency reports.

In attacks shortly before dawn, Iraqi jet fighters bombed targets described by Information Minister Latif Nassif Jassim as "the headquarters of the rulers" in Tehran. At midmorning Iraq also attacked Ilam, in western Iran, claiming hits on "selected targets" in the city center. It also struck several other smaller cities.

Iraqi aircraft carried out two more raids against Tehran late Sunday, Agence France-Presse reported from Tehran. The attacks plunged the city into darkness for the second straight day.

Iran said late Sunday that at least 13 persons had been killed in the raids on Tehran but that it was too early to know the casualty toll from the other cities, Reuter reported.

Jassim said in an interview that attacks also will be stepped up against shipping in the Persian Gulf.

In early April the two countries waged a campaign against each other's cities, with Iraq bombing Tehran and other cities, and Iran apparently using Soviet-made 1960s-vintage rockets to attack Baghdad. That ended after U.N. mediation.

The current offensive appears to be a significant escalation by Iraq after a lull of several weeks, but Jassim said no land offensive is planned unless "we are forced to do that."

Instead, Iraq is relying on what foreign military observers here calculate is air superiority of 4 to 1 against Tehran. Western diplomats estimated that Iraq has more than 400 operational fighters and bombers while Iran has about 100 and possibly fewer.

Jassim, other Iraqi officials and a strongly worded statement yesterday by the Revolutionary Command Council under President Saddam Hussein cite several specific objectives in the current offensive:

* First, and most broadly, Iraq aims to force Iran into negotiations to end the war that has dragged on for 56 months at a cost of tens of thousands of lives on both sides. Jassim reiterated Iraq's demands that Iran withdraw to the border recognized before the war; that it agree to a cease-fire on land, on water and in the air; that it agree to an exchange of prisoners of war, and that it begin unconditional negotiations on the basis of noninterference in the internal affairs of Iraq or other nations.

Iran repeatedly has insisted that it will not stop fighting until the government of Saddam Hussein is removed. It also insists that Iraq be declared the original aggressor in the war that began in September 1980.

* Iraq's officials say they expect the current air offensive to stimulate internal opposition in Iran to the regime of Ayatollah Ruhollah Khomeini. "It is likely that the streets in Iran are explosive," Hassan Tawalba, director general of foreign relations at the Information Ministry, said, citing economic and social pressures generated by the war. "We believe such shocks will separate Khomeini from his bases and foundations."

* The new air attacks also are portrayed as retaliation for alleged Iranian-supported terrorism in the area. The attempted assassination of the emir of neighboring Kuwait yesterday is cited as a specific example. The command council statement, released last night before the bombing began, vowed to "strike strongly all hideouts of evil and aggression in Tehran as a punishment for . . . the crimes they committed and chaos and subversion exported by them."

* The new air offensive also is preemptive, according to officials here. Jassim warned that "any Iranian offensive will be entombed, and Iran will witness a catastrophe because our preparations are beyond their expectations and beyond their imagination."

Jassim would not discuss specific figures, but he did confirm that Iraq has observed a buildup of heavy Iranian concentrations along the border in recent weeks. Some foreign military observers here said in the past few days that they believed a new Iranian push was imminent. According to these sources as many as 23 Iranian divisions have massed along the border.

The foreign military observers also say that large convoys of tanks and other heavy military equipment moved north two weeks ago in apparent anticipation of an Iranian offensive along the central front south of Mandali and east of Baghdad, as well as another possible push in the southern swamps around Basra.