The minister said the two sides will communicate again later this week to discuss further details.
The decision to pay the ransom comes despite the government's efforts to facilitate the hostages' release and to even prepare special forces for a strike on Abu Sayyaf.
The Al Qaeda-linked group, which is based on the island of Mindanao, hijacked the Indonesian-flagged tugboat and the barge Anand 12 while en route to the Philippines from Banjarmasin in East Kalimantan province. The barge was later found abandoned.
The Abu Sayyaf group is also believed to be behind the hijacking of two more Indonesian ships, the tugboat TB Henry and the barge Cristi on Friday last week. Another four Indonesian crewmembers were kidnapped in the incident. Six other crewmembers on board the two ships were released.
Luhut said Indonesian authorities and their counterparts in the Philippines are still investigating the whereabouts of the four Indonesians kidnapped this weekend.
The Abu Sayyaf is notorious for kidnappings, beheadings, bombings and extortion. The group has also been a major influence on other terror groups in Southeast Asia, including those in Indonesia.