SINGAPORE — President Xi Jinping of China met with President Ma Ying-jeou of Taiwan on Saturday in the first-ever encounter between leaders of the neighbors and longtime rivals, an act both sides described as a breakthrough gesture meant to promote peace and mutual prosperity.

Mr. Xi and Mr. Ma began their brief talks with a handshake that went on for more than a minute, with both men smiling broadly and turning side to side so the hundreds of reporters in the meeting room at the Shangri-La Hotel in Singapore could document the moment. The meeting is a high point in the two leaders’ efforts to bridge the divisions of civil war and decades of animosity.

When the two men sat down to start their talks, Mr. Xi spoke first and said their encounter was a historic step that opened a new chapter in relations between the two sides. He said that the people of China and Taiwan were compatriots, “one family with blood that is thicker than water.”

“Respected Mr. Ma Ying-jeou, good afternoon,” Mr. Xi said in comments that were broadcast live on Chinese television.