Indonesia's largest ride-hailing, payments and services company, Go-Jek, plans to expand its presence across more markets in Southeast Asia in the near future, according to its president.

After officially launching its services in Vietnam earlier this week, Go-Jek is building up its operations in Thailand and working with regulators in Singapore and the Philippines, Andre Soelistyo told CNBC on Friday.

"Thailand is coming very soon ... the team is already working to operationalize the product," he said, adding that, for Singapore and the Philippines, "we're still working it out with local regulators, local teams to make sure that all the requirements are being checked properly, before we do the expansion."

Earlier in May, Go-Jek announced that it would invest about $500 million to move into the four markets over the next several months. The company said it would provide "technological support and expertise" to local founding teams that would then work on gaining traction in each of those countries.

The mobile app that was launched in Vietnam is called Go-Viet and is now available in the major cities of Hanoi and Ho Chi Minh City. On that app, users can book two-wheel rides and make use of courier services — the company said there are plans to introduce four-wheel ride-hailing, food delivery and digital payment services on the application in the future.

Soelistyo said the decision to launch first in Vietnam had several motivations, including its cultural similarity to Indonesia, and the high social media penetration rate.