BORACAY, Philippines—The U.S. Senate’s passage of fast-track legislation has injected fresh momentum into talks on a landmark Pacific trade deal, with negotiators saying they are in the final stages of discussions after more than five years of wrangling.

U.S. Trade Representative Michael Froman said he feels good about progress on the deal, which would lower tariffs and set environmental and intellectual property rules, among other things, for 12 nations including the U.S. and Japan that together account for about 40% of the global economy.

“We’re very much in the endgame,” Mr. Froman told reporters during a meeting of trade ministers of the 21-member Asia-Pacific Economic Cooperation forum on the resort island of Boracay. He declined to specify a timetable for concluding the talks.

On Friday, the U.S. Senate passed so-called fast-track legislation, which would help conclude the Trans-Pacific Partnership deal with Japan and 10 other countries. The fast track, or trade-promotion authority, means that this pact and others would be held to an up-or-down vote in Congress without amendments.

Mr. Froman, who arrived in Boracay on Saturday after seeing through the fast-track measure in the Senate, said he looked forward to working with House legislators to get the pact passed “as soon as possible.”

The fast-track bill faces a test in the House in June. Still, TPP trade ministers said over the weekend that clearing a first hurdle in the Senate is a positive sign.

The Senate’s vote was a “welcome development” and could set the stage for completion of the trade pact “in the coming months,” said New Zealand Trade Minister Tim Groser.

Other ministers signaled they were also ready to push forward with talks: “Mexico is ready to wrap up negotiations,” Economy Minister Ildefonso Guajardo said.

Many of the TPP founding nations—the U.S., Japan, Australia, Brunei, Canada, Chile, Malaysia, Mexico, New Zealand, Peru, Singapore and Vietnam—have been reluctant to hold concluding talks on the trade pact without guarantees that U.S. lawmakers wouldn’t subject it to changes.

Trade ministers in recent days canceled a meeting in Guam after most of the countries involved in creating the TPP objected to discussions without assurance of the fast-track legislation in the U.S., Chile’s Deputy Trade Minister Andres Rebolledo said.

At a breakfast Sunday morning, trade ministers in Boracay discussed the status of the Guam negotiations, but didn’t set a timetable for a next round of minister-level meetings, officials with knowledge of the meeting said. Several officials said a host of issues being discussed in Guam remain to be resolved.

The trade pact is controversial in the U.S. and in many founding countries for being too far-reaching in measures including stringent intellectual property rights, among other things.

Mr. Rebolledo described the pact as a necessity for Chile, which depends heavily on foreign trade and is the only TPP member that has existing bilateral trade agreements with all other members.

“When you’re a country like this, you need rules. You need that everyone fulfills the rules, especially the big countries,” he said.

Write to Ben Otto at [email protected]