The shooting on Monday adds a wrinkle to a complicated relationship between Russia and Turkey — rivals going back centuries — which over the last year have switched from being adversaries to pseudo-allies over the bloody war in Syria.
Erdogan was enraged with Russia when it first entered the war, and Turkey shot down a Russian warplane over its airspace in late 2015.
But Erdogan made a turnaround with Russia almost immediately after the coup attempt. On the night of the coup, Russia tipped off Erdogan about unusual movements among Turkish military units, Bremmer said, potentially saving the Turkish president's life.
In the meantime, the assassination of Karlov is unlikely to dramatically alter anything in the war-wracked region. A senior Russian parliamentarian told the Interfax news agency that the assassination will not disrupt previously scheduled talks between Russia, Turkey and Iran in Moscow.
"The Russians will express their gravest possible concerns, and Erdogan will use this as an excuse to crack down on political enemies as much as possible," Bremmer said.
A Turkish security official on Monday already was linking the assassination to a U.S.-based cleric whom it has previously blamed for its civil unrest, usually before Ankara makes waves of arrests.
McCaffrey described the killing of one ambassador as unfortunate but only a "footnote" in the scope of the wider war.
"The much larger issue is a half million dead in Syria," he said.
Turkey has struggled with a steep drop in foreign investment and a plunging currency that has lost 20 percent of its value against the dollar this year. The iShares MSCI Turkey ETF and VanEck Vectors Russia ETF were trading lower Monday.
—Reuters contributed to this report.
Correction: This story was revised to correct that Turkey's Kurds live mostly in the eastern part of the country.