Former prime minister Tony Abbott crossed paths with US President Barack Obama at an event attended by dozens of other people rather than having a "private dinner" as reported.

Mr Abbott, who has been in the US for several days, met Mr Obama at a lunch of the Alfalfa Club, an informal gathering of high-powered businesspeople and politicians, according to multiple sources.

The impromptu meeting was reported in News Corp papers as the pair having "met privately", suggesting Mr Abbott was still being actively courted and received by the Obama administration in what would be a source of frustration for his successor Malcolm Turnbull.