Both countries also signed two other MOUs to continue the Peace Corps programme, which involves the US providing social and economic development assistance, and to expand educational ties that have seen thousands of young leaders participating in exchange programmes.
The MOUs were signed on Tuesday (Dec 14) by Indonesia's Foreign Minister Retno Marsudi, Education Affairs Minister Nadiem Makarim and US Secretary of State Antony Blinken, who was in Jakarta on the first leg of a four-day trip to South-east Asia.
Mr Blinken told a media briefing later the three agreements would bring cooperation between the two countries to another level.
Referring to the MOU on maritime cooperation, Ms Retno said that it would also cover conservation and fisheries management, as well as maritime safety and navigation.
"In order to strengthen our security cooperation, we agreed to establish a two-plus-two dialogue mechanism between senior officials from each ministry of foreign affairs and defence," Ms Retno added.
The US has also offered to to work with Indonesia to deal with the Covid-19 pandemic and ensure a strong post-pandemic economic recovery.
"President (Joe) Biden asked me to come here to advance our work together on a number of critical issues that includes stopping the Covid-19 pandemic," Mr Blinken said.
The US has donated more than 25 million doses of vaccines to Indonesia, and the latest shipment arrived on Tuesday. On top of this, the US is also providing US$77 million (S$105.4 million) in pandemic relief assistance.
Ms Retno said that Indonesia hoped both countries could also cooperate in the development of mRNA-based vaccine technologies.
Pfizer-BioNTech and Moderna are among the companies that have successfully developed Covid-19 vaccines using this technology.
In Indonesia, Mr Blinken met President Joko Widodo at the Jakarta presidential palace on Monday, and expressed the US' commitment to strengthen its partnership with Indonesia, including in economic development and infrastructure development.
During the meeting, which was described by Ms Retno as "warm and open", Mr Widodo expressed his appreciation for the support given to Indonesia by the US amid the Covid-19 pandemic.
By Wahyudi Soeriaatmadja