MOSCOW — From Moscow to Washington to capitals in between, the past few days have showcased the way President Vladimir V. Putin of Russia nimbly exploits differences between the United States and its allies.

Yet recent events have also highlighted the downside to Mr. Putin’s geopolitical escapades and accentuated where he falls short on matters of vital importance to both himself, and ordinary Russians.

President Trump had barely finished catapulting a belligerent tweet and new sanctions at Turkey on Friday before Mr. Putin was working the phone with his Turkish counterpart, President Recep Tayyip Erdogan.

It was vintage Putin, showcasing his seizure of any opportunity to divide the West.

But at the same time, the Western sanctions he hoped to get lifted have only been tightened this past week, pushing the ruble down to its lowest levels in years.