BEIRUT, Lebanon (AP) _ The nation's Cabinet met Thursday for the first time in seven months and said it wanted to reopen Beirut airport and take control of ports now operated illegally by militia groups.

Militiamen, meanwhile, clashed nearby on the Green Line and a girl was reported killed. And Christians and Moslems joined in a nationwide strike to protest soaring prices, brought on by acute economic problems.

''The Cabinet agreed on the needed arrangements and economic solutions to the pressing crisis,'' a government spokesman said in a short statement after the four-hour session. He did not disclose further details of the meeting in the heavily guarded Parliament building on the dividing Green Line.

Parliament Speaker Hussein Husseini said the conferees called for the reopening of the airport and the handing over to government authorities of all illegal ports in Lebanon.

Beirut airport has been closed since Feb. 1 after foreign insurance companies refused to cover aircraft using the facility.

Government officials say the closure of a half dozen militia-run ports would allow authorities to re-establish tax collection.

Husseini, who attended the meeting in his capacity as representative of the nation's legislators, said the conferees also decided to launch a government- subsidized medicine plan and a special department to look after the estimated one million Lebanese displaced from their homes during the civil war.

Prime Minister Rashid Karami said his 10-member, half-Moslem, half- Christian Cabinet scheduled another meeting on the economic crisis for April 30.

All Cabinet ministers attended the session except for Druse warlord Walid Jumblatt, who holds the public works portfolio. No reason was given for his absence.

As the Cabinet session began, Moslem and Christian militiamen fought with machine guns across the dividing line in south Beirut. Police said one girl was killed and three civilians were injured.

The Cabinet meeting, the first in 215 days, proceeded as government offices, banks newspapers, schools, bakeries, gasoline stations and other businesses closed for the three-day strike.

The strike was called earlier in the week by the 250,000-strong General Confederation of Labor, which said the action would be called off later in the day if the Cabinet reaches ''decisions or arrangements capable of containing the economic decline.''

Karami's Cabinet last met in September, when its members failed to agree on a new power-sharing formula to end the 12-year-old civil war.

Moslems, who make up about 55 percent of Lebanon's four million people, have been fighting for an equal share of power with the nation's Christians, who have dominated the government, army and judiciary since independence from France in 1943.

The Lebanese pound, once the most stable currency in the Middle East, lost 98 percent of its value in the past 12 years. It rated 2.5 to the U.S. dollar before the 1975 outbreak of the civil strife. Its current exchange rate is 120 to the dollar.

The government-set minimum monthly wage of 3,200 popunds shrank in value from the equivalent of 1,280 dollars in 1975 to its record low of 26 dollars this month in a country that imports 80 percent of its needs.

The 12 years of violence have claimed at least 125,000 lives, raised inflation to 200 percent a year and upped unemployment to the unprecedented rate of 20 percent.

''I really wish success for the government in discussing the economic crisis,'' said Adel Bouhsali, a grocer in Moslem west Beirut. ''Prices have gone up to unbelievable levels. Some of my usually good customers are no longer able to buy enough milk for their children.''