Peking has ordered the immediate closing of three Vietnamese consulates in southern China, Hanoi Radio announced last night. The move marks a sharp decline in the already rapidly deteriorating relations between the two Communist nations.

The official Vietnam News Agency published a note to the Chinese from the Vietnamese Foreign Ministry saying the demand to close this consulates "in the shortest time" was "another extremely serious act of the Chinese side." The consular offices in the capitals of the southern provinces of Yunnan and Kwangtung and the autonomous region of Kwangsi have been operating for more than 20 years.

Although Peking made no immediate response to the Vietnamese announcement, a second diplomatic note published by Hanoi indicated China was retaliating for Hanoi's decision to delay establishment of a new Chinese consulate in Vietnam and impose a strict deadline on a planned sea evacuation of Chinese refugees from Vietnam.

The announced three-month deadline means China will be unable to open a consulate in Ho Chi Minh City (formerly Saigon), the South Vietnamese city with the largest ethnic Chinese population, until after the evacuation is over.

Diplomatic sources have reported a reinforcement of Chinese military forces in its provinces bordering Vietnam during the last few months and a tightening of military preparation on the Vietnamese side. But only a few border skirmishes have been reported during that time, and diplomats in Peking and Hanoi still discount the chance of any open military clash.

The Vietnamese demanded, however, that Peking "protect (the) lives, property and legitimate interests of the "Vietnamese residents under the charge" of the three consulates being closed.Each of the border provinves has an ethnic Vietnamese minority.

Thousands of ethnic Chinese are still pouring over the border from Vietnam in apparent response to harassment of Chinese that has escalated during Vietnam's war with Cambodia. Phnom Penh is strongly backed by Peking. China has reported a total of more than 133,000 refugees crossing into China so far.

It has begun to dispatch ships for a sea evacuation from Vietnamese ports of those Chinese who wish to and are permitted to leave Vietnam starting today. Chinese officials have estimated that about 300,000 of Vietnam's estimated 1.8 million Chinese residents would eventually flee to China by land or sea, more than the total number of Vietnamese refugees who have fled the Indochinese nation since the Communist victory in 1975.

The second Vietnamese note to China released by the Vietnam News Agency yesterday announced that the sea evacuation could take no longer than three months and that each Chinese ship could spend no more than three days during each stop at three designated Vietnamese ports, Haiphong in Northern Vietnam, Quinhon in central Vietnam and Ho Chi Minh City.

If 100,000 of Ho Chi Minh City's estimated 1 million Chinese residents seek evacuation, at least one Chinese ship would have to call there each day to meet the deadline.

Vietnam has said that it will allow anyone who wants to leave the country to board the Chinese ships but the diplomatic noted indicated it would have sole discretion of over who would get an exit permit. The Vietnam has made little effort so far to stop the flow of refugees across the Chinese border, indicating an apparent willingness to rid itself of a troublesome minority and not to further exacerbate its worsening relations with its powerful northern neighbor.

But the Chinese exodus deprives the Vietnamese of a substantial, and in some case highly trained, labor force at a time of severe economic trouble. There have been reports from refugees reaching here that Hanoi is not issuing exist permits to any healthy young male Chinese.

Refugees from Ho Chi Minh City who have reached here on special flights say the residents of Vietnam's largest Chinese community have in many cases had their bags packed for weeks in anticipation of the Chinese sea evacuation.

Many of Ho Chi Minh City's Chinese are former shop keepers who have had their businesses closed by strict new anti-capitalist regulations in Vietnam and would not be expected to particularly enjoy life in China either. Yet they seem anxious to take what is now the only convenient escape route out of a country whose people are now suffering severe shortages of food and other staples.

China has sent almost daily accounts over its official news agencies of Vietnamese persecution of ethnic Chinese and of Peking's efforts to ease the plight of refugees. The propaganda appears designed to win favor with the 20 million overseas Chinese whose loyalty is important to Peking in its ongoing dispute with the Nationalist Chinese in Taiwan.

The Vietnamese note to the Chinese Ministry of Foreign Affairs released yesterday indicated that it was responding to a June 16 note from Peking. It said, "Following a series of arrogant and unreasonable actions against Vietnam, the Chinese government has decided that the three Vietnamese consulates general should stop their activities and all their staff should return to their country in the shortest time . . . This is an extremely absurd act. This unilateral decision of the Chinese side has further deteriorated the relations between the two countries and seriously undermined the traditional friendship between the two peoples. The Chinese side must bear full responsibility for this situation."

Although the Chinese provided the Vietnamese Communists with substantial military and economic aid during their war to take over the South, Peking has always been suspicious of the unusually close ties between Hanoi and China's arch enemy, Moscow. Vietnam revealed last week that Peking had canceled 72 construction projects it had been funding in Vietnam and had withdrawn "a great number of Chinese specialists" in retaliation for what it said was persecution of Chinese in Vietnam.

The Chinese have spoken bluntly in recent weeks of Soviet efforts to turn Vietnam against China. The Vietnamese have made veiled criticisms of Chinese support for Cambodia and made more specific charges of Peking's failure to help thousands of ethnic Chinese allegedly massacreo after the Communist takeover in Cambodia in 1975.