Mr Subianto said he and Mr Dutton discussed "the possibility of Australia opening their training areas for the participation of Indonesian units to be training together with Australia".
Mr Dutton said Australia and Indonesia were bolstering their security cooperation in "an increasingly contested region".
"Our renewed defence cooperation arrangement will see Australia and Indonesia step up our training initiatives, our joint training initiatives, and defence operational activities over the coming years."
Mr Dutton also said Australia would provide 15 Bushmaster protected mobility vehicles to Indonesia for use in peacekeeping operations.
He said defence education programs would also be stepped up, with cadets from Indonesia's armed forces studying at Australian defence education facilities.
Taliban urged to respect human rights
Mr Marsudi said Indonesia was closely monitoring the situation in Afghanistan and hopes the country will not be used as "a breeding and training ground for terrorist organisations and activities that threaten peace and stability in the region".
On Tuesday, the Taliban announced an all-male interim government that includes many veterans of their hard-line rule in the 1990s and 20-year battle against US-led forces.
The two foreign ministers on Thursday urged the Taliban to respect the human rights of women and girls in Afghanistan.
Indonesia has suffered a series of militant attacks since bombings on the tourist island of Bali in 2002 killed 202 people, mostly foreigners, including 88 Australians. The Bali bombings were blamed on the al-Qaeda-linked Jemaah Islamiah network.
In the following decade, Indonesian security forces backed by the US and Australia crushed Jemaah Islamiah, killing leaders and bomb makers and arresting hundreds of militants.
But a new threat has emerged in recent years from Islamic State group sympathisers, including Indonesians who travelled to the Middle East to fight with the group.
"Indonesia has a significant role to play as a Muslim country with a strong voice on these issues," Ms Payne said in a joint video news conference with Mr Marsudi, Mr Dutton and Indonesian Defence Minister Prabowo Subianto.
Source: Indonesian Ministry of Foreign Affairs
Australia calls for 'healthy competition' in Indo-Pacific
Ms Payne and Mr Dutton arrived in Jakarta on Wednesday for the first of a series of meetings with foreign and defence ministers in Indonesia, India, South Korea and the United States to underscore Australia's role in the Indo-Pacific region, where China's influence and military power are growing.
Their trip will also prepare for Prime Minister Scott Morrison's visit to Washington later this month to meet with US, Indian and Japanese leaders in the Quadrilateral Security Dialogue.
China has called the so-called Quad an attempt to contain its ambitions.
Ms Payne described the Indo-Pacific region as the most dynamic, innovative and prosperous in the world.
"To maintain that prosperity and security, we welcome a region that supports a level playing field based on rules and norms to ensure healthy competition, rather than competition that risks sliding into instability or conflict," she said.
The four ministers agreed to cooperate in defence, cybertechnology and countering terrorism and violent extremism, and in fighting the coronavirus pandemic.
Surging infections have strained Indonesia's healthcare system as it struggles to roll out vaccinations.
Australia has provided it with 1 million vaccine doses, 1,000 ventilators and more than 800 oxygen concentrators and cylinders.