Federal Reserve Board Governor Lael Brainard speaks at the John F. Kennedy School of Government at Harvard University in Cambridge, Massachusetts, U.S., March 1, 2017. REUTERS/Brian Snyder

NEW YORK (Reuters) - A U.S. rate hike is probably coming soon though the Federal Reserve may want to delay if inflation remains soft, an influential Fed governor said on Tuesday, adding she also backs shrinking the bond portfolio “before too long.”

In a mostly upbeat speech that mapped out a very gradual reduction in the central bank’s bond holdings, Fed Governor Lael Brainard said she is however most concerned with a lack of progress in pushing inflation up toward a 2-percent goal in recent months.

“It would be reasonable to conclude that further removal of accommodation will likely be appropriate soon,” she said without mentioning the Fed’s next policy meeting on June 13-14.

Yet “if the tension between the progress on employment and the lack of progress on inflation persists, it may lead me to reassess” that prediction, added Brainard, a dovish permanent voter on U.S. monetary policy. “The apparent lack of progress in moving core inflation back to 2 percent is a source of concern.”

The U.S. central bank has raised interest rates twice since December and investors widely expect it to tighten policy again next month, and once more before year end.

Those expectations were boosted slightly after a government report earlier on Tuesday showed monthly inflation rebounded somewhat. Still, on a year-on-year basis the Fed’s preferred inflation measure rose 1.5 percent in April - which Brainard called a “considerable shortfall” from the goal.

The Fed has also signaled it plans later this year to begin shedding some of its $4.5 trillion in bond holdings, most of which it amassed in the wake of the financial crisis and recession. It would initially set a low cap on the securities allowed to run off, and raise that every three months, under the plan.

Brainard largely agreed, saying the process should be set on “autopilot” and be “calibrated” to the differences between maturing Treasury- and mortgage-backed assets. She also suggested it would likely begin this year, noting the process could be halted and even reversed if the U.S. economy faced an “adverse shock.”

“Predictability, precision, and clarity of communications all argue in favor of focusing policy on the federal funds rate as the single active tool,” she said. “The balance sheet essentially would remain subordinate to the federal funds rate.”