ISTANBUL—Turkey faces a historic crossroads as lawmakers prepare to debate a controversial bill introduced this weekend to concentrate power in the office of the presidency, at a time when the nation is polarized about whether President Recep Tayyip Erdogan is a force for stability or insecurity.

Hours after Mr. Erdogan’s ruling party deputies submitted the legislation that would fundamentally reshape this North Atlantic Treaty Organization member’s democracy, twin suicide bombings ripped through central Istanbul, killing at least 38 civilians and policemen. Kurdish insurgents claimed the attack targeting Turkish security forces.

“Whenever Turkey takes a positive step for the future, we are immediately faced with a response of blood, lives, violence, chaos—delivered by terrorist organizations,” Mr. Erdogan said after the attacks, suggesting a correlation between them and the proposed constitutional amendments.

The bill before parliament, essentially a referendum on Mr. Erdogan’s rule, threatens to deepen political cleavages that have all but destroyed the ability to rule Turkey through consensus—even as the country faces myriad other critical threats. These include fears of a prolonged economic slump, a counterterrorism fight both at home and across its borders—as well as the fallout from the failed coup this summer.

Mr. Erdogan has been ruling by decree under a state of emergency since July, and over the last four months tens of thousands of Turks have been arrested and purged from their state jobs as alleged national security threats. A sizable number of those detained include political opponents and lawmakers.