In a show of courage and good sense, Turkey’s government has announced a plan to grant long-denied rights to its Kurdish minority, and, it is hoped, finally end an insurgency that has cost more than 40,000 lives.

Kurds compose as much as 20 percent of Turkey’s population, yet for decades the government banned their political parties and denied them the most basic cultural rights, including the right to use their own language. This mistreatment helped fuel Kurdish demands for independence and two decades of bloody attacks by the Kurdistan Workers Party, or P.K.K.

Although some 12,000 militants are still hiding in northern Iraq along the Turkish border, the P.K.K. has been steadily losing popular support. The new initiative is designed as further pressure and incentive for the group to disband. Last year, Parliament legalized private Kurdish language courses and created the first public television channel in Kurdish. New regulation lets Kurdish prisoners speak to visitors in their native language.

Parliament is now debating an initiative that would allow the Kurdish language to be used in all broadcast media and political campaigns. It would restore Kurdish names to thousands of towns that were given Turkish ones. And it would establish an independent committee to fight discrimination and investigate torture allegations.

There are other trends that are very worrisome, including Prime Minister Recep Tayyip Erdogan’s attempts to shut down independent news media. But Mr. Erdogan has shown sound leadership with his plan for the Kurds, despite fierce opposition from nationalist politicians. For Turkey to fulfill its potential as a secular Muslim democracy, he will have to keep battling the nationalists and others to make additional political and economic reforms, without sacrificing free political debate.

The United States and other Western countries that have long pushed Turkey to become more democratic should encourage Mr. Erdogan to keep pressing ahead. Most important, Europe must finally make clear that if Turkey bolsters its democracy and respects the rights of its minorities, it will be welcome in the European Union.