US President Donald Trump said on Twitter that he had a "long and very good call" with Chinese President Xi Jinping and that a possible trade deal between the two sides was progressing well. In late November, the two countries had agreed to halt additional tariffs, hold fresh talks and reach an agreement within 90 days.
China is Southeast Asia's biggest trading partner and its trade war with the United States, which has cost both sides billions of dollars in losses, also hit Southeast Asian stock indexes, all of which ended 2018 in the red. Singapore's index rose 0.3 percent on Monday, with top gainer Thai Beverage PCL advancing 3.4 percent. Lender DBS Group Holdings Ltd firmed 1.1 percent.
Malaysia's benchmark was boosted by industrial conglomerate Sime Darby Berhad, which rose 3.4 percent, and tourist resort operator Genting Malaysia Berhad , which added 1.3 percent.
Singapore's index has shed over 10 percent this year, while Malaysian stocks were among the region's better performers with a 5 percent decline.
Singapore's market will trade for shorter hours on account of New Year's Eve, while Malaysian markets have regular trading hours.