ROME—Prime Minister Silvio Berlusconi on Monday was in 11th-hour talks aimed at saving his conservative coalition as investors renewed pressure on the premier to step down and allow a new government to steer the country out of Europe's debt crisis.

Over his 18 years as the leading man of Italian politics, the 75-year-old Mr. Berlusconi has survived sex scandals and corruption trials. But on Tuesday, Italy's controversial leader faces what is likely to be the biggest test of...