Secretary of State Marco Rubio indicated on Tuesday that the United States may resume its funding of a global vaccines alliance that Health Secretary Robert F. Kennedy Jr. pulled the United States out of last year, an unusual public rebuke of Mr. Kennedy’s involvement in matters of global health.

Testifying on Capitol Hill, Mr. Rubio told senators that President Trump had asked the State Department to allow Mr. Kennedy to “play a leading role” in the decision on whether to fund Gavi, an organization that provides immunizations for low-income nations and maintains the global Ebola vaccine stockpile.

But Mr. Rubio suggested in pointed testimony that he was reclaiming control of the U.S. relationship with Gavi, which has historically been managed by the State Department.

The State Department is “going to re-engage on the issue of Gavi,” Mr. Rubio told the Senate Foreign Relations Committee. He said that the department was not going to “yank” the matter from Mr. Kennedy, a longtime vaccine skeptic, or ignore “his points of view.” But he said that a few weeks ago, he had made the decision to resume management of the relationship.

About Mr. Kennedy, Mr. Rubio added: “I wouldn’t use the word defer, but we have certainly allowed him to play a leading role in determining what we’re going to do next. But right now, we’re sort of at a stage where we are going to re-engage. We need to drive this to an outcome.”

Mr. Rubio’s reassertion of authority is part of a broader effort by the State Department to reclaim control of global health from the Department of Health and Human Services, said J. Stephen Morrison, a global health expert at the Center for Strategic and International Studies in Washington.