Romania's prime minister was dismissed today in a major government reshuffle that appeared to reflect an attempt by President Nicolae Ceausescu to find new solutions for the country's growing economic and political problems.

The shake-up follows several months of mounting political intrigue and economic difficulties including food shortages, corruption and a serious foreign debt problem.

An emergency meeting of the Central Committee of the ruling Communist Party approved the resignation of Ilie Verdet as premier and his replacement by a senior party official, Constantin Dascalescu. The new prime minister announced government changes that included dropping Cornel Burtica as minister of foreign trade.

Both Verdet and Burtica are said to be related to Ceausescu by marriage. Their purge, in the view of some observers, could signify the beginnings of a breakup of the extended family dynasty that rules Romania, a Warsaw Pact nation of 22 million people.

Verdet, who was appointed premier three years ago and was regarded as Ceausescu's number two, was given the largely ceremonial position of one of three vice chairmen of the collective presidency or state council.

News of the changes was inexplicably delayed by official Romanian news media, but it was carried by the Yugoslav state news agency Tanjug in a dispatch from Bucharest that was monitored here. Dascalescu was said to have asked the defense, interior and foreign ministers to remain.

Frequent government and Communist Party shake-ups have been a feature of Ceausescu's 17-year rule. A highly skillful politician, he reshuffles top aides regularly to prevent anyone from building up an independent power base and to find sacrificial victims for his government's failures.

Romania and Poland have frequently been linked as "the sick men of the Soviet Bloc." Western diplomats in Bucharest, the Romanian capital, note, however, that the political traditions of the two countries are quite different and, despite widespread complaints and grumbling, Romanians are unlikely to join a protest movement such as Solidarity in Poland.

Ceausescu's political difficulties stem largely from the failure of his strategy of rapid industrialization that was to have turned Romania from a backward peasant society into a developed country by the middle of this decade. Romanians have become accustomed to seeing a vision of prosperity receding beyond the horizon, and last year Ceausescu publicly admitted that it had been a mistake to neglect agriculture in favor of heavy industry.

But there have been political scandals, too, such as the one that led last month to the dismissal of Education Minister Aneta Spornic and two of her deputies. They were officially accused of "lack of vigilance" over an institute for transcendental meditation that had an office in Bucharest and was apparently patronized by many bureaucrats and intellectuals.

The full details of this curious affair are still shrouded in mystery, but a Romanian magazine recently charged that the real purpose of the institute was to undermine the Communist Party and state.

Three other deputy ministers were removed from office last week for alleged "violations in connection with foreign economic projects." They included Alexandru Margaitescu, secretary of state at the Foreign Trade Ministry and a principal adviser to Burtica. The others were Enachu Sirbu and Emilian Mihailescu, of the Agriculture Ministery.

Dascalescu, the new prime minister, has been a trusted associate of Ceausescu for some years in the party's decision-making Political Executive Committee. He was head of the party's agricultural department in the mid-1970s and recently supervised the party's organizational section.

Verdet is understood to be married to one of Ceausescu's sisters and Burtica to one of the president's nieces.

Other prominent Ceausescu family members include his wife Elena, who is first deputy prime minister and a member of the Political Executive Committee, and their son, Nicu, who heads the party's youth league.