WASHINGTON — In launching a military strike just 77 days into his administration, President Trump has the opportunity, but hardly a guarantee, to change the perception of disarray in his administration.

The attack will also shape the meeting next week between Secretary of State Rex W. Tillerson and President Vladimir V. Putin of Russia — the first face-to-face encounter between the Russian leader and a member of the Trump administration.

Before the strike on a Syrian air base on Thursday night, the meeting had been expected to be dominated by the investigation into Russia’s cyberattacks and the interference in the presidential election on Mr. Trump’s behalf.

But the Syria action gives the Trump administration an opportunity to demand that Mr. Putin either contain or remove Syria’s leader, Bashar al-Assad, or else Mr. Trump will expand the limited American military action — and quickly — if the Russian president fails to do so.