The immigration minister, Peter Dutton, has rejected calls for independent monitoring of conditions for asylum seekers and refugees in offshore processing facilities, saying the level of support provided now is sufficient.

The president of the Human Rights Commission, Gillian Triggs, told ABC’s Lateline program on Monday night that there needs to be independent oversight of detention centres, as question marks remain over the fate of a young Somali refugee who alleges that she became pregnant after being raped on Nauru.

“We clearly need some form of independent monitoring system so that we can have objective, fair processes to understand exactly what’s going on here and to give all parties a fair opportunity to get the facts straight,” Triggs said.

Dutton rejected the calls. “The opportunity is there for people to travel,” he told reporters. “We have a number of visits, including from Red Cross, UNHCR and others to the detention centres and that regime, that level of oversight.

“The way in which the oversight regime operates at the moment, the way in which we are providing support with taxpayers’ money to people who do need medical assistance, that is the system that will be continuing into the future.”

In Senate hearings on Tuesday, Triggs said that the commission would be happy to take on the job of independent monitor, but that the refusal of the Nauruan government to allow commissioners into the country would pose significant jurisdictional problems.

“I can’t go there, can’t get a visa,” she said.

The jurisdictional question of whether an independent Australian body can offer oversight of a facility in another sovereign country created an impediment to the Human Rights Commission playing a stronger role in offshore detention, Triggs said.

Entry to the facilities on Nauru and Manus Island “does not depend on decisions of the Australian government but on two sovereign governments,” the attorney general, George Brandis, told estimates.

Also during estimates, Triggs revealed that the Human Rights Commission is in talks with the secretary of the Department of Immigration and Border Protection, Michael Pezzullo, on including human rights modules in training for detention centre staff.

The training would take in practical applications such as the use of force.

“Do you handcuff people when you are taking them to Nauru? Do you handcuff children and people in wheelchairs,” Triggs said, offering examples of what could be covered in the training.

“We have a lot to offer in terms of training, and the secretary was very open to that,” she said, adding that discussions were moving quite quickly and that Pezzullo was keen to get started soon with an enhanced training program.

Giving border force staff and immigration department officials enhanced training would give the federal government a stronger role in managing detention centres, Triggs said, as staff members could be put on the frontline alongside private management companies that currently manage the centres.

Dutton praised border force staff, who he said performed professionally and to a high standard.