Pacific nation and USA-dependent Marshall Islands has stood tall amid the New York skyscrapers at the 80th United Nations General Assembly.

At the Assembly, Marshall Islands president Dr Hilda Heine called on the UN to take responsibility for past decisions which harmed her country while demanding the inter-global organisation urgently act on climate change.

In her speech, President Heine reflected on what Marshallese people had endured following occupation from Japanese traders and later their colonial administration, which lasted 30 years between world wars until the islands were captured by US forces in 1944.

She reminded the world's leaders of a destructive history which once featured regular nuclear tests carried out near Marshallese low-lying atolls and reef islands – predominantly focused around Bikini Atoll – during the UN's trusteeship period of the territory from 1946 until 1958.

Records show the Americans conducted 67 nuclear tests, under the UN flag, in the pursuit of their own nuclear development.

"Marshallese pleas to the Trusteeship Council to stop nuclear testing were disregarded," Dr Heine said.

"We were told we were safe, but we were not."

Despite evacuating 167 people off the Bikini Atoll in a forced relocation by the US military, Dr Heine said the nuclear legacy still affects the health of many Indigenous Austronesian citizens after devastating their own social fabric.

They were originally moved to Rongerik Atoll, east of their Bikini Atoll, however their new home had inadequate resources to support the population and when people started to experience starvation within 18 months, they were forced to move to a third, larger atoll.

The islanders' traditional lifestyle was based on subsistence living of cultivating plants, eating shellfish and fresh fish, which was unable to be sustained on Rongerik.

"Our communities seek justice, a clean environment and safe return to their homes," Dr Heine said.

The descendants of the Bikini islanders, a tight knit cultural group under the custodianship of clans and chiefs, are prohibited to return to their homeland over ongoing nuclear contamination fears despite the amounts of radiation slowly declining.

Scientists have found dangerously high levels of radioactivity in well water after past islanders voluntarily returned home in 1972.

The bodies of relocated residents were found to be carrying abnormally high levels of concentrated nuclear fission after living on Bikini Atoll for just six years.

Dr Heine asked the UN to publicly recognise its involvement and failings, but did not seek out compensation nor restitution.

The UN had been created just months earlier in October of 1945, not long after ratifying the US' rights to conduct the nuclear testing.

"The UN should be capable of delivering a contemporary acknowledgment and an apology for what took place in its name and under its flag," she said.

The Marshall Islands signed the Compact of Free Association with the US in 1979 and given its independence just seven years later, despite relying on US foreign aid for survival.

Dr Heine's message also focused on the long-term future for the Marshall Islands.

She warned climate change is now the biggest security threat to nearby small Micronesian states such as the Marshalls.

The nation's 20 coral atolls were once formed on submerged volcanic peaks millions of years ago, but no longer exist after climate change has affected the small, ocean islands.

The highest peak of the Marshall Islands is now barely 10 metres above sea level, which makes the atolls especially vulnerable to further sea-level rise.

"If I could find a louder alarm for other Pacific Islands than my words today, I would sound it," Dr Heine said.

"Only urgent action at scale can protect our people and our future."

The Marshallese had followed a traditional belief system which revered the islands and their environment.

She called out rich western countries for not delivering on their climate financial promises.

"Promises don't reclaim land in atoll nations like mine," she said.

"Those things require serious money."

Dr Heine also voiced strong support for a moratorium on deep seabed mining.

The Marshall Islands, which has a small black pearl farming industry, has already banned the seabed mining practice in its own waters while urging others in the region to follow suit.

In comparison, Tonga's government has signed an agreement to approve seabed mining to commence in the not-so-distant future while the Cook Islands have plans to explore an option in a deal signed this year with the People's Republic of China.

"We cannot afford to destroy what we don't yet understand," Dr Heine said.

Dr Heine also raised concern about small-island states in the fourth world akin to the Marshall Islands being ignored for making a stand on the world stage.

"Our voices carry the weight of lived truth," Dr Heine said.

"The hope for our future is in nations committed to peace, justice and multilateralism.

"Let us not wait any longer."