"Erdogan and Putin have mostly economic interests that bind them," Giraldi said on Tuesday.
Turkey had infuriated Russia by supporting rebels in Syria seeking to topple President Bashar Assad, Giraldi noted.
The failure of the coup means Erdogan will have to be cautious about using his military in any foreign adventures, including in Syria, Giraldi predicted.
"As long as Turkey abstains from direct military involvement in Syria… the relationship will continue to be somewhat strained but on balance correct," he maintained.
By contrast, US-Turkish relations were clearly heading into a period of increased strain, Giraldi noted.
Giraldi said he also expected Erdogan to put increasing pressure on US diplomatic and intelligence personnel operating in Turkey.
"I do not believe the United States will give in but will instead offer various compromises that will not satisfy Erdogan. The relationship is in trouble and will not improve as long as Erdogan continues to be in charge," he concluded.
Philip Giraldi is executive director of the Council for the National Interest, a group that advocates more even-handed US government policies in the Middle East.