MADRID, June 27 (Reuters) - North Atlantic Treaty Organization (NATO) leaders will urge Turkish President Recep Tayyip Erdogan to lift his veto over Finland and Sweden's bid to join the military alliance when they meet for a three-day summit on Tuesday (Jun 28), as the West strives to send Russia and China a signal of resolve.

Taking place in the shadow of Russia's war in Ukraine, the Madrid gathering comes at a pivotal moment for the transatlantic bond after failures in Afghanistan and internal discord during the era of former United States president Donald Trump, who threatened to pull Washington out of the nuclear alliance.

Negotiations among an often-fractious organisation are still under way, diplomats said, but leaders also hope to agree to provide more military aid to Ukraine, increase joint defence spending, cement a new resolve to tackle China's military rise and put more troops on standby to defend the Baltics.

Spain, whose king will host a dinner for leaders, is also pushing for more NATO focus on the southern flank to address migration and militant groups in the Sahel region of Africa.

The leaders of Australia, New Zealand, Japan and South Korea are expected to attend part of the summit, part of a broader US strategy for a more assertive Western presence in the Indo-Pacific region to counter China.

"We will do more to ensure we can defend every inch of allied territory, at all times and against any threat," NATO Secretary-General Jens Stoltenberg said in a speech last week.

Although British and US officials have advised against a Baltic request for permanent multinational forces in the region, the summit is likely to settle on a compromise of promising rapid reinforcements.

Germany has already said that it will put more troops at the ready to defend Lithuania should Russia seek to seize NATO territory, and Britain is expected to do the same for Estonia, while Latvia is looking to Canada to pledge more troops there.