WASHINGTON—Indonesia’s President Joko Widodo said on Monday that his country will seek to join 12 other Pacific nations in the Trans-Pacific Partnership free-trade agreement.

Speaking at the White House on Monday, Mr. Widodo laid out the economic rationale for his country’s participation in the tentative trade deal through a translator.

“Indonesia is an open economy. And with the largest population in Southeast Asia, we are the largest economy in Southeast Asia and Indonesia intends to join the TPP,” said Mr. Widodo.

Negotiators completed the trade agreement earlier this month, capping a yearslong process to create a regional trade bloc and lower market barriers and access.

The current version of the pact comprises a dozen countries, including the U.S., Japan, Canada, New Zealand and Australia. Those nations account for about 40% of global output.

Mr. Widodo was in Washington for a meeting with President Barack Obama, where the two leaders focused on climate change, energy and regional security issues.

The tentative agreement needs to be ratified by the individual countries. In the U.S., the White House will need to win support in Congress, which in recent history has narrowly approved trade deals, overcoming deep skepticism among rank and file Democratic lawmakers about the benefits of trade deals.

Indonesia and other countries that have expressed interest in joining the trade pact likely will have to wait until it has been ratified by the initial group of countries.