The CSRs, worth about $7 billion this year, compensate insurers for offering qualified low- and moderate-income Obamacare customers discounts in their their out-of-pocket health costs, including co-payments and deductibles. Those discounts are mandated by law.
Most people who buy health coverage on HealthCare.gov and other government-run insurance marketplaces qualify for the reduced charges. Almost 6 million people qualified last year.
Trump, peeved about the failure of his fellow Republicans in the Senate to pass an Obamacare replacement bill had threatened to end CSR payments to insurers.
The president previously has tried to use the threat of ending the cost-sharing payments as a means to force passage of a bill to replace Obamacare.
But just as he has done every month since taking office, Trump on Wednesday agreed to let them continue.
The Affordable Care Act, as Obamacare is formally known, requires insurers to offer reduced out-of-pocket charges customers of individual health plans if those people earn less than 250 percent of the federal poverty level, or less than $30,150 per year for a single person.
A report by the Kaiser Family Foundation found that for people who earn between 150 percent and 200 percent of poverty "the average deductible is reduced to $809, a savings of $2,800" each year.
The ACA also says that the federal government will compensate insurers for the money they do not collect in co-payments, coinsurance and deductibles from the qualified customers.
Next year the subsidies are projected to be worth $10 billion to insurers.
But the GOP-led House of Representatives sued the Obama administration in 2014 for paying the reimbursements without having Congress appropriate the money for it. Republicans in Congress, opposed to Obamacare, refused to vote for such spending.
A federal judge in 2016 upheld the House's challenge to the legality of the payments. But she agreed to let the payments continue as the Obama administration pursued an appeal of the decision.
The election of the avowed Obamacare foe Trump as president set the stage for his administration to drop the appeal of the decision, and to end the payments. But Trump didn't drop the appeal.
Instead, the president and Congressional Republicans have agreed to allow the payments to continue in the face of warnings from insurers and insurance experts that health plans would have to increase their premiums by 20 percent or more to cover the loss of the reimbursements.
That's because insurers, even if they did not get the reimbursements from the federal government, are legally obligated to offer the cost-sharing reductions to eligible customers.
Sen. Alexander, chairman of the Senate Health Committee, in a statement said, "Congress now should pass balanced, bipartisan, limited legislation in September that will fund cost-sharing payments for 2018 as well as make section 1332 of the Affordable Care Act work better to give states more flexibility in approving insurance policies."
"These two actions will help make insurance policies available at affordable prices. Congress owes struggling Americans who buy their insurance in the individual market a breakthrough in the health-care stalemate," Alexander said.
"The Senate health committee begins hearings on stabilizing the individual market the first week of September. Congress should act before the end of September to keep insurance available at a reasonable cost during 2018."
Leslie Dach, director of the Obamacare advocacy group Protect Our Care Campaign, said, "We are glad the administration is making these crucial payments to help lower out of pocket costs and increase deductibles for August."
"However, this cat-and-mouse game every month has to stop," Dach said. "As the nonpartisan CBO and Kaiser Family Foundation concluded in recent reports, just the threat of not making these payments has caused insurers to jack up prices next year and has injected uncertainty into the market for consumers and insurers alike."
"Canceling these payments altogether, as President Trump has repeatedly threatened, will increase premiums by 25 percent in 2020 and increase the deficit by nearly $200 billion over the next decade," Dach said. "It's time for the Trump administration and Republicans in Congress to stop sabotaging our health care and work with Democrats to improve it."