In the days since Mr. Obama spoke out on Friday, Mr. Trump has kept up the argument. On Twitter, he retweeted a supporter’s message: “Watching @BarackObama take credit for @realDonaldTrump successes is disgraceful.”

On Sunday, quoting another supporter, the president tweeted: “Barack Obama talked a lot about hope, but Donald Trump delivered the American Dream. All the economic indicators, what’s happening overseas, Donald Trump has proven to be far more successful than Barack Obama.”

Growth since the recession of 2008-09 has been slower than after any other recession since World War II, and the distribution of the growth has been less equal than in the past. But growth has also been unusually steady, set in motion by Mr. Obama’s extraordinary economic interventions early in his presidency. This is now one of the longest periods of uninterrupted economic growth in American history, with 95 straight months of job creation.

In the 19 months starting after Mr. Trump’s inauguration, the economy has created 3.58 million new jobs — but that is still shy of the 3.96 million created in the last 19 months of Mr. Obama’s presidency. The nation’s economy has grown at a steadily higher pace in the past year than it did during the end of Mr. Obama’s term, reaching an annualized rate of 4.2 percent in the second quarter of this year. But the last time it was that high was in 2014 — when Mr. Obama was in charge.

Moreover, even the faster growth under Mr. Obama or Mr. Trump remains modest compared with some previous recoveries. During the first half of this year, the economy grew at a 3.3 percent annualized pace, slower than every year of the Reagan recovery, which averaged 4.4 percent between 1983 and 1989.

Mr. Trump has some particularly compelling bragging points, though. Unemployment is now at 3.9 percent, close to the lowest it has been in a half-century, and joblessness among African-Americans and other minorities has also fallen to historically low rates. The stock markets have reached record highs as well. All of these trends began when Mr. Obama was president. Mr. Trump’s supporters argue that he turbocharged them with his tax cuts and deregulation, defying critics’ predictions that he would wreck the economy.

“I can say that the economy was in fine shape at the end of the Obama administration, despite what President Trump sometimes asserts,” said N. Gregory Mankiw, a Harvard economist and chairman of the president’s Council of Economic Advisers under George W. Bush. “The tax cuts likely made it stronger, while worsening the long-term fiscal imbalance. Reasonable economists can and do disagree about how much impact the tax plan has had.”