Lukas Enembe travelled to Port Moresby to attend celebrations to mark PNG's 43rd anniversary of independence.
Mr Enembe, who was recently re-elected as governor of Indonesia's eastern-most province, led a delegation of 21 people to Port Moresby.
He was invited by the governor of PNG's National Capital District, Powes Parkop.
Mr Parkop has this month spoken out about human rights abuses in Indonesia's Papua region, widely known as West Papua.
He was critical of both PNG and Indonesian governments for not confronting the West Papuan rights issue openly.
The Governor also called for more integrated economies and closer people-to-people ties.
Earlier, Mr Parkop commended PNG prime minister Peter O'Neill for "trying his best to address that sore point", referring to the rights issue.
But he called for more discussion at the international level about the plight of West Papuans.
"It is important that we talk about the West Papua issues with the Indonesian Government and at the international forum," he said.
"We have to address it openly and maturely. And I would like to see an open and mature type of discussion to take place."
In response, PNG's Foreign Minister Rimbink Pato said the two countries had forged a close relationship where all issues of mutual interest, including sensitive border matters, were discussed in a constructive way.
The minister said PNG had welcomed the Indonesian government policy under President Joko Widodo to take a development-led approach to the Papuan Provinces rather than a security-led approach.