BALI, Indonesia — The annual Group of 20 summit began on Tuesday under the shadow of the war in Ukraine and concerns about a possible global recession, as leaders of some of the world’s wealthiest nations and biggest emerging markets push for a coordinated response to the threats.

As the group of 19 countries and the European Union gathers on the Indonesian island of Bali, Russia’s invasion of Ukraine, the U.S.-China rivalry and a resurgence of authoritarianism are testing alignments in the existing world order.