Under President Trump, the United States led the world in reducing carbon-dioxide emissions in 2019, but don’t expect Greta Thunberg to give him a hug any time soon.

International Energy Agency data released earlier this month showing that U.S. emissions dropped by 2.9% last year failed to make an impression with Democrats, environmentalists and climate activists, who either shrugged off the data or argued that Mr. Trump’s climate-denialism was somehow thwarted.

“U.S. carbon emissions declined last year in spite of every effort by the Trump administration to prop up dirty energy,” said David Doniger, senior strategic director of the Climate & Clean Energy Program at the National Resources Defense Council, in an email.

Such responses drew an eye-roll from Republicans.

“Have they given the President credit for anything since taking office? It’s not surprising,” said Austin Hacker, spokesman for the Republicans on the House Natural Resource Committee.

“The facts speak for themselves,” he added. “Under President Trump, the United States has finally become an energy exporter and a global leader in emissions reductions.”

At the same time, the climate skeptics who have backed Mr. Trump’s push to boost coal, bring back manufacturing, and pull out of the Paris agreement warned against doing backflips over the continued U.S. decline in greenhouse gases.

Myron Ebell, director of the Center for Energy and the Environment at the free-market Competitive Enterprise Institute, said that cheering the reduction surrenders the field to the climate-change movement.

“I have very contrary feelings about it,” Mr. Ebell said. “I understand why various people want to take credit for it because it annoys and challenges other countries, which are not making reductions in carbon-dioxide emissions. But on the other hand, it concedes the point that there’s something good about lowering carbon-dioxide emissions.”

Under the Trump administration, the nation has become a net exporter of oil and natural gas, years ahead of predictions, while U.S. emissions have continued an overall decline that began in 2005 as natural gas, spurred by the shale and fracking revolution, and renewable energy replace coal in electricity generation.

“I don’t see that it’s a good thing. It’s just a fact,” Mr. Ebell said. “The other thing I would point out is that if the Trump strategy is successful, we should see a continuing return of energy-intensive manufacturing in this country, and if that’s the case, emissions are going to start going up again at some point.”

The IEA data released Feb. 11 showed that after two years of increases, global carbon-dioxide emissions flattened in 2019 as developed nations, led by the United States, the European Union and Japan, reduced their output even as emissions continued to rise in the world’s two most-populous nations — China and India.

“US emissions are now down almost 1 Gt from their peak in the year 2000, the largest absolute decline by any country over that period,” the report said. “A 15% reduction in the use of coal for power generation underpinned the decline in overall US emissions in 2019.”

The IEA data coincided with Jan. 17 figures from the U.S. Energy Information Administration, which found that energy-related carbon-dioxide emissions fell by 2.1% in 2019, and predicted a 2.0% decline in 2020 and a 1.5% drop in 2021.

Last week, the Environmental Protection Agency released preliminary data showing power-plant emissions in the lower 48 states fell in 2019. Annual output of sulfur dioxide alone declined by 23%, dropping below one million tons for “the first time in modern history,” said EPA Administrator Andrew Wheeler.

“Under President Trump, our economy continues to grow, and we are enjoying ever-improving air quality,” said Mr. Wheeler in a statement. “Through state and federal fulfillment of the Clean Air Act, as well as advances by the power sector, we have seen significant reductions in key pollutants.”

Environmentalists warned that the Trump administration was “rowing in the wrong direction” with its deregulation push.

“Coal is being out-competed in electricity markets by gas, wind, solar, and energy efficiency,” Mr. Doniger said. “Electric cars are making inroads in vehicle markets. But to meet the climate crisis, we must move to clean energy and away from fossil fuels much faster than market forces will do on their own.”

Rachel Cleetus, policy director of the climate and energy program at the Union of Concerned Scientists, called the latest emissions decline a “bright spot,” but said the pace needs to hasten to meet the U.N. Intergovernmental Panel on Climate Change targets.

“Their long-term projection is by 2050, they’re seeing just a 4% below 2018 number, and that’s of course wildly off course from what the IPCC and the other science is showing is necessary to limit the impacts of climate change,” Ms. Cleetus said.

She noted that emissions from the transportation sector have now overtaken those from power plants.

“Obviously the end goal here is to cut emissions deeply, so if all we do is just grow in one place and cut in another, we’re not actually achieving the goal that we need,” Ms. Cleetus said. “We need to bend the whole curve down.”

Mr. Ebell disagreed.

“I know they say we’re in a climate emergency, but we’re only in a climate emergency if we live in a fantasy world of computer models,” he said.

“If you think those are the reality, we’ve got a problem,” he said. “If you believe the historical temperature data and the real-world measured impact, we don’t have a crisis, and it’s not even clear we have a problem.”

One drawback with touting emissions reductions in the developed world is that it may only mean that the manufacturing base has been outsourced to countries like China.

“What we’re learning is that trying to reduce emissions is playing whack-a-mole,” Mr. Ebell said. “You push them down somewhere, and they come up somewhere else.”

James Taylor, director of the center for climate and environmental policy at the free-market Heartland Institute, argued that any mild rise in global temperatures has brought with it benefits, including improvements in agricultural production and human mortality.

“I agree it can be a trap to tout the reduction in U.S. carbon-dioxide emissions as good news because it’s not necessarily beneficial. It may even have a net harm,” Mr. Taylor said.

At the same time, he said, it’s worth pointing out that the decline has come not as a result of government crackdowns on energy and industry, but rather from technological innovations such as fracking, driven by the private sector and a favorite target of liberal climate hawks.

“I think it is important to note that for people who do believe in a climate crisis, and who do believe the world should take action, that the United States is already doing more than its fair share — without the large government-centered programs that the environmental left always advocates,” he said.