WASHINGTON — On the campaign trail, Donald J. Trump falsely accused President Barack Obama of founding the Islamic State. He said Mr. Obama “did not get it,” in terms of fighting the extremist group that is based in Iraq and Syria, and vowed to obliterate them on the battlefield.

But in the Trump administration’s first major announcement of its still-nascent plans to defeat the militants, Secretary of State Rex W. Tillerson on Wednesday closely parroted Mr. Obama’s strategy. His comments came as talk of fighting the Islamic State was overshadowed by an attack in London that killed four and injured 40. It was not immediately clear who was responsible for the attack, or if the Islamic State was linked to it.

“The great commonality among we who have gathered today is a commitment to bringing down a global force of evil,” Mr. Tillerson said at the start of a conclave of the 68-nation coalition to defeat the Islamic State that was held at State Department headquarters.

In his 20-minute speech, Mr. Tillerson noted that over the past year, the flow of foreign fighters into Iraq and Syria had dropped more than 90 percent, and that 75 percent of the Islamic State’s online propaganda had been eliminated. Both gains occurred largely on Mr. Obama’s watch.