At a rally in Michigan a little over a week ago, President Trump assured his supporters that he had kept his promise to abolish the Affordable Care Act — even though Congress had failed to repeal the Obama-era health law.

“Essentially, we are getting rid of Obamacare,” Mr. Trump said, reminding a cheering crowd that the individual mandate that required most people to have health insurance or pay a penalty was scrapped as part of the Republican tax bill he signed into law last year. “Some people would say, essentially, we have gotten rid of it.”

But despite Mr. Trump’s longstanding desire to unwind the signature legislative achievement of his predecessor, many parts of the Affordable Care Act remain in place. And the Trump administration is even enforcing some of its provisions more aggressively than President Barack Obama did — a reality that has enraged business groups and Republicans in Congress who still want the law officially repealed.

While the individual mandate may be dead, the employer mandate — the requirement that many companies offer health insurance to their workers or pay a penalty — is very much alive. Under Mr. Trump, the Internal Revenue Service has been pursuing companies that fail to comply with the mandate and, according to the agency, was sending penalty notices to more than 30,000 businesses around the country.

Business groups are pushing for the I.R.S. to stop enforcing the mandate and House Republicans, who voted to repeal much of the Affordable Care Act a year ago, have proposed legislation to eliminate it. But most Democrats oppose major changes to the law and the Republican leaders in the Senate have shown no interest in tackling health care after last year’s stinging defeat.

The employer mandate requires companies with more than 50 full-time employees to provide health benefits to eligible employees or face fines of more than $2,000 per worker. The Congressional Budget Office predicted that these fines would total $12 billion in 2018.

The I.R.S. is working on settlements with some of the businesses that have had technical issues or paperwork glitches, according to David Kautter, the Treasury Department’s assistant secretary for tax policy and the acting I.R.S. commissioner.

But other companies that have failed to provide insurance will face stiff fines.

“I think it is horribly unfair and unjust,” Representative Jody Hice, a Republican from Georgia who has been a leading voice in the opposition to the employer mandate, said at a hearing where Mr. Kautter testified in April. “What I am asking at this point is for the I.R.S. to continue not to enforce it, as is what took place under the Obama administration,” he said, referring to a reprieve that was granted while businesses and the government sorted out compliance details.

Some lawyers contend that the I.R.S. is on shaky ground in trying to enforce the employer mandate penalties, arguing that the government has not followed proper procedures, like notifying employers that they were in violation of the law.

“The Affordable Care Act and federal regulations clearly state that a health insurance exchange must notify an employer that one or more employees qualified for premium tax credits before the I.R.S. can impose penalties,” said Christopher E. Condeluci, an employee benefits lawyer. “Most of the employers subject to penalties for 2015 never received the notices required under the law.”

E. Neil Trautwein, a vice president of the National Retail Federation, said some penalties resulted from an employer’s failure to check a particular box on a government form indicating that it had offered coverage to eligible employees.

In one case, Mr. Trautwein said, a $20 million penalty was imposed on a restaurant chain because one of its vendors had failed to check the proper box. “The penalty was negotiated down to zero,” Mr. Trautwein said. “It was an inadvertent mistake in filling out a complicated new form.”

John D. Arendshorst, an employee benefits attorney at Varnum, said he has been busy fielding questions from companies that have received proposed assessments from the I.R.S. and said the government has shown a willingness to reduce penalties when appropriate. In one case, a business with about 500 employees received an assessment for $1.9 million. That was ultimately reduced to $20,000 because the penalty was caused by a computer error.

“They were shocked for sure,” Mr. Arendshorst said of the initial penalty letter. “They felt it was a big mistake and it turned out to be.”

Under the Affordable Care Act, the employer mandate was to take effect in 2014. The Obama administration delayed enforcement for an additional year after employers said they needed more time to comply with rules requiring them to report on the coverage they provided to employees. And the Treasury Department needed more time to clarify the requirements. It was not until late last year that the I.R.S. had the capacity to determine which businesses were in violation of the mandate, and the agency is just now sending penalty letters related to the 2015 tax year. Penalty letters for the 2016 and 2017 tax years are expected to follow soon.

Republicans criticized the decision to begin enforcing the mandate as a parting shot by the former I.R.S. commissioner John Koskinen, whom they had previously assailed over the agency’s scrutiny of conservative nonprofit organizations. While Mr. Trump had issued an executive order that called for easing the Affordable Care Act’s regulations, the Treasury Department, which oversees the I.R.S., said it was required to abide by the law and enforce the employer mandate.

Mr. Koskinen pushed back against the idea that he was attempting to punish conservatives by jump-starting enforcement of the employer mandate, and he said that companies had been given plenty of notice that they needed to provide insurance to their employees.

“The I.R.S. does not have the authority not to collect the money,” Mr. Koskinen said in an interview, adding that there was no reason to hold off on penalizing companies. “Delaying wouldn’t accomplish anything except delay.”

Business groups have been lobbying Congress to repeal the employer mandate or to get the I.R.S. to stop enforcing it. They argue that companies did not receive sufficient notice that they needed to comply with a provision of the health law that had not been enforced for seven years.

“The employer mandate always existed to support the individual mandate,” said Jim Klein, president of the American Benefits Council. “There’s no logic or fairness in having an employer mandate in the absence of having an individual mandate.”

Mr. Klein said he would like to see a legislative fix to address the situation.

Mr. Trump himself has added to the confusion over the mandate by repeatedly asserting that the Affordable Care Act had been essentially eliminated because Republicans did away with the individual mandate.

“It’s yet another reason why the employer mandate needs to go,” Representative Kevin Brady of Texas, the Republican chairman of the House Ways and Means Committee, said of the penalties.