Sydney — The United States and small Pacific island nations are trying to take the heat out of what's been headlined a ''tuna war'' in the region. The dispute, which has remained a far-flung obscurity in the United States, nonetheless has the US State Department concerned. It is anxious not to damage relations with member nations of the South Pacific Forum, a group of small island countries plus Australia and New Zealand.
In the eye of the current storm is the Solomon Islands, population 250,000, a former British colony which got independence in 1978. In July, it used its lone patrol vessel to seize a San Diego-registered vessel, the ''Jeanette Diana.''
Like other islands in the area trying to protect one of their few resources, the Solomon Islands have declared that foreign tuna-fishing vessels cannot fish within 200 miles of their territory.
The Solomons government has let it be known it was considering opening its ports to Soviet fishing vessels, but diplomats discounted this as no more than an expression of anger at US tuna vessels' incursions into its 200-mile limit.
The US recognizes that Soviet penetration in the mini-nations has been minimal, despite proffered aid sweeteners from Moscow to allow diplomats and ships greater access to the area.
Unlike a similar seizure by neighboring Papua New Guinea in 1982, which resulted in a vessel being released swiftly when the US tuna industry paid compensation to the Papua New Guinea government, the Solomon Islands seizure bubbles on. The hapless Jeanette Diana itself remains under guard (its crew was allowed to return to the US) in the Solomon Islands, its future for the moment uncertain.
It is a big issue in the country and Prime Minister Solomon Mamaloni's government shows no sign of climbing down. It tried to sell the helicopter-equipped vessel for about $3.5 million.
But no prospective buyers turned up in the capital city of Honiara, after an American bank that owned a mortgage on the vessel advertised worldwide that prospective buyers should keep away since the purchase would not be legally theirs.
Australia, the dominant economic and political power in the region, is working behind the scenes, according to sources in the region, to bring an end to the squabble. The aim is to find a face-saving solution for the Honiara government and ensure relations with the US remain sound.
The view expressed by one Honiara government official that the Jeanette Diana incident ''wasn't an isolated one'' is accepted through the region.
For this reason, Prime Minister Bob Hawke's Australian government is quietly arguing for a treaty as soon as possible: Only with rights and obligations spelled out on all sides, it believes, will a repetition of the Jeanette Diana incident be avoided.
Representatives of 12 Pacific countries and the United States met recently in Suva, the capital of the Fiji Islands. They agreed to work toward formulating a multilateral treaty to cover tuna fishing within 200-mile economic zones.
A treaty would spell out how much fish US vessels could take from these waters, and what the islands - some of the world's poorest nations - would be paid.
US sources say a treaty would take precedence over present US law, which commits the US to ending trade with countries that seize US tuna vessels in 200 -mile zones.
The legislation, for which the US tuna fishing industry has lobbied, is based on American nonrecognition of these zones where migratory tuna are concerned.
The effect on the Solomon Isands economy of US trade sanctions will be minimal, officials there argue, because trade between the two nations is currently slight.
The country's total exports in 1982 were less than $60 million. Fish, timber, and copra are key exports. The main buyers are Japan, Britain, Sweden, the Netherlands, and Australia.