WASHINGTON—President Trump on Monday called for the Federal Reserve to sharply cut interest rates and again criticized the central bank’s chairman for a “horrendous lack of vision,” while reiterating his belief that the U.S. economy is strong. The president said in a pair of tweets Monday morning that the Fed should cut its benchmark interest rate by at least a full percentage point and resume its crisis-era program of buying bonds to lower long-term borrowing costs. Such moves would typically be considered only when the economy faces serious peril, which Fed officials don’t believe to be the case. White House officials have said in recent days that they don’t believe the U.S. is headed toward a slowdown. Larry Kudlow, the director of the National Economic Council, said Sunday that there were no signs of a recession and that the White House is considering tax cuts aimed at the middle class, which Mr. Trump floated before the 2018 midterms but didn’t ultimately pursue. White House aides said Monday they are examining other proposals to bolster the economy. Among the ideas being discussed is a cut in the payroll tax, but two people familiar with the matter said they didn’t expect such a proposal to be pursued. One White House official said the president hasn’t endorsed the idea. Another White House official said Monday that “more tax cuts for the American people are certainly on the table, but cutting payroll taxes is not something under consideration at this time.” Payroll taxes, which are separate from the federal income tax, fund Medicare and Social Security and come out of workers’ paychecks, paired with employer levies. For 2011 and 2012, employees’ Social Security payroll tax rate was cut to 4.2% from 6.2% as a revamped tax break that was started in the 2009 stimulus law. Congress let that payroll-tax cut expire. In his latest criticism of Fed Chairman Jerome Powell, who goes by Jay, Mr. Trump said Monday that the U.S. economy “is very strong, despite the horrendous lack of vision by Jay Powell and the Fed.” If the Fed cut its benchmark rate by at least a percentage point and perhaps launched a new bond-buying program, the president tweeted, “our Economy would be even better, and the World Economy would be greatly and quickly enhanced.” Last month, the Fed trimmed rates by a quarter percentage point to a range between 2% and 2.25%, citing risks from slower global growth and unexpectedly soft inflation. Mr. Powell is navigating the Fed toward more rate reductions and is scheduled to speak Friday at the Kansas City Fed’s annual conference in Jackson Hole, Wyo. Investors are hoping Mr. Powell will provide more insight into his policy approach at a time when the economic outlook is buffeted by heightened risks and as the Fed is being publicly attacked to a degree that is virtually without precedent in its 105-year history. A rate cut of the magnitude Mr. Trump called for Monday, which hasn’t happened since the global financial crisis in late 2008. Interest-rate futures are pricing in a 95% chance that the Fed will reduce rates by a quarter percentage point at its Sept. 17-18 meeting. The probability of the benchmark federal-funds rate being lowered by a full percentage point before the end of the year is estimated at 2.2%, according to CME Group. Mr. Trump’s Twitter dispatch Monday came after he returned from a 10-day vacation at his golf resort in Bedminster, N.J., during which financial markets experienced wild swings and the Dow Jones Industrial Average suffered its biggest single-day loss of the year. While the president and his advisers have blamed the swoon on the Fed pushing interest rates too high last year, many economists and executives say Mr. Trump’s own trade policies are responsible for spooking financial markets, hurting business investment and weakening the global economy. Before Mr. Trump’s Aug. 1 announcement of the latest round of tariffs on Chinese goods, the Dow was less than 1% below its all-time high.