Trump's inauguration address rattled off a list of crowning American feats such as ending slavery, launching into space, and the moment they "split the atom".

The mayor of Nelson in New Zealand's South Island seized on the sub-atomic slight, pointing out that work to split the atom was actually pioneered by Kiwi-born physicist Ernest Rutherford.

"I was a bit surprised by new President Donald Trump in his inauguration speech about US greatness claiming today Americans 'split the atom' when that honour belongs to Nelson's most famous and favourite son Sir Ernest Rutherford," mayor Nick Smith wrote on social media.

Credited with splitting the nucleus of an atom during experiments at UK's Manchester University in 1917, Rutherford was "the first to artificially induce a nuclear reaction by bombarding nitrogen nuclei with alpha particles", Smith said.

He added that he would invite the incoming US ambassador to visit the Rutherford memorial in Nelson, population 50,000, "so we can keep the historic record on who split the atom first accurate".

Widely regarded as the "father of nuclear physics", Rutherford was awarded the Nobel Prize for Chemistry in 1908 for earlier work on radioactivity.

He remains one of New Zealand's most famous sons, and his face still adorns the country's $100 bill.