NUSANTARA, Indonesia — Indonesian President Joko Widodo spent his first night in the eagle-shaped palace of the country’s proposed new capital, Nusantara, ahead of official meetings on Monday, as the outgoing leader works to allay fears about the beleaguered infrastructure project.

Jokowi, as the president is known, has been rushing to complete as much of the new capital as possible before he steps down in October, despite Nusantara facing multiple construction delays, a lack of foreign…