Most Southeast Asian stock markets closed higher on Tuesday, with Philippines gaining the most after President Rodrigo Duterte apologised for his "hurting words" about two tycoons associated with some of the biggest companies in the country.

President Duterte apologised to the Ayala family, the owners of Ayala Corp, and to Manuel Pangilinan, the CEO of Metro Pacific Company, offering an olive branch to settle a costly regulatory row.

Shares of Ayala Corp and Metro Pacific Investments Corp surged 14.7% and 13.6%, respectively, helping the Philippine benchmark end 1.8% higher after gaining as much as 2.4% earlier in the session, the most since April 17.

Meanwhile, most other markets in Southeast Asia rose as investors found hope in the phased reopening of some economies that were earlier hard hit by the coronavirus pandemic.

"The oscillating sentiment once again shifted towards the positive end, underpinned by reopening hopes that looks to relieve some of the frayed nerves from concerns over renewed US-China tensions," Jingyi Pan, market strategist at IG said in a note.

Malaysian stocks ended about 1% higher, boosted by Petronas Chemicals Group and Axiata Group, which gained 2.8% and 1.9%, respectively.

The country's central bank on Tuesday slashed its key interest rate by 50 basis points to the lowest since 2009 and left the door open for further cuts to protect the trade-reliant nation's economy from prolonged, pandemic-driven damage.

Bucking the trend, Thai stocks shed 1.8%, pressured by Minor International, down 5.2%, and Hana Microelectronics, which fell 3.5%.