So far, the blockade is not working, and the crisis looks set to worsen. Secretary of State Rex W. Tillerson flew back to Washington on Thursday after days of apparently fruitless shuttle diplomacy in the region. The foreign ministers of Germany, France and Britain have also intervened, without success.

The blockading nations — Saudi Arabia, Egypt, the United Arab Emirates and Bahrain — insist that Qatar is using an open-door policy to destabilize its neighbors. They say that Doha, rather than the benign meeting ground described by Qataris, is a city where terrorism is bankrolled, not battled against.

Qatar’s self-identity as a center of refuge dates to the 19th century, when its desolate and semilawless territory offered sanctuary to outlaws, pirates and people fleeing persecution across the Arabian Peninsula.

“It’s always been this place where waifs and strays and unwanted people ended up,” said David B. Roberts, the author of “Qatar: Securing the Global Ambitions of a City-State” and an assistant professor at King’s College in London. “There was no overarching power on the peninsula, so if you were wanted by a sheikh, you could escape to Qatar and nobody would bother you.”

In the 19th century, Qatar’s founding leader, Jassim bin Mohammed Al Thani, called it the “Kaaba of the dispossessed” — a reference to the revered black cube at the Great Mosque in Mecca, Islam’s holiest site, and a figurative way of describing Qatar as a lodestar for those seeking refuge.

That national trait turned into a policy for Al Thani’s descendants, who since the mid-1990s have thrown open Qatar’s doors to dissidents and exiles of every stripe. Doha has welcomed Saddam Hussein’s family, one of Osama bin Laden’s sons, the iconoclastic Indian painter M. F. Husain and the Chechen warlord Zelimkhan Yandarbiyev, who was assassinated in the city by Russian secret agents in 2004. (The agents were caught and later extradited to Russia.)