WASHINGTON — About 6.4 million people have signed up for health insurance next year under the Affordable Care Act, the Obama administration said Wednesday, as people rushed to purchase plans regardless of Republican promises that the law will be repealed within months

The new sign-ups — an increase of 400,000 over a similar point last year — mean the health care coverage of millions of consumers could be imperiled by one of the first legislative actions of Donald J. Trump’s presidency. Hundreds of thousands of other people who took no action will be automatically re-enrolled by the federal government in the same or similar plans, officials said, and their coverage could be threatened as well. Consumers still have until the end of January to enroll.

Sylvia Mathews Burwell, the secretary of health and human services, said the number of signups was remarkable in view of “headwinds” created by premium increases for 2017 and by the uncertainty of the entire health law after Mr. Trump takes office on Jan. 20.

Americans remain divided over President Obama’s most significant legislative achievement, even as 20 million people have gained coverage under the law and the percentage of those without insurance has dropped to record lows. Mr. Trump and Republican leaders of the House and the Senate have vowed to repeal the 2010 law as one of the first legislative actions of the Trump era.

To lay the political groundwork, Republicans have portrayed the law as collapsing under its own weight, unable to hold down health costs or provide the insur

Day After a Deadly Blast

Wreckage from Tuesday’s explosion at a fireworks market near Mexico City. Workers worry the market won’t be rebuilt. Page A8.

WASHINGTON — Eric Trump said on Wednesday that he had decided to stop directly soliciting contributions for his charitable foundation, which supports causes like the fight against childhood cancer, because he now recognizes that his status as the president-elect’s son means that donors could try to use him to gain access to his father.

As unfortunate as it is, I understand the quagmire, Mr. Trump said in an interview Wednesday evening. You do a good thing that backfires.

His move followed public criticism of an online auction that the Eric Trump Foundation had sponsored offering a chance to have coffee with his sister Ivanka. The criticism intensified over the weekend after an invitation was drafted offering a hunting trip with Eric Trump or his brother Donald Jr. in exchange for donations of $500,000 or $1 million to a new charity that friends of Eric Trump had created this month with his apparent consent, according to legal documents.

Ethics experts had begun to compare Eric Trump’s charitable

WASHINGTON — Presidentelect Donald J. Trump seemed to suggest on Wednesday that the deadly truck attack on a Christmas market in Berlin vindicated his proposal during the presidential campaign to bar Muslims from entering the United States

You know my plans, Mr. Trump said to reporters who asked whether the attack on Monday, in which a Tunisian is being sought, would cause him to reevaluate his proposals to create a Muslim registry or to stop Muslim immigration to the United States. All along, I’ve been proven to be right. One hundred percent correct.

It was not clear whether Mr. Trump was reaffirming his muchcriticized call for a wholesale ban on Muslim immigration or his subsequent clarification that he would stop only those entering from countries with a history of Islamic extremism. As with many of his pronouncements since his election last month, the remarks, delivered on the blustery front steps of his Mar-a-Lago estate in Florida, were cryptic and left room for broad interpretation

But hours later, one of his advisers said he was only restating his most recent position.

BERLIN — Searching the cab of the tractor-trailer that plowed through a Christmas market in Berlin, the authorities made two startling discoveries: a badly bruised body with stab and gunshot wounds, and the wallet of a Tunisian labeled a security threat who was supposed to have been deported months ago.

The identity of the Tunisian, Anis Amri, immediately alarmed intelligence officials from Europe to Washington. German officials acknowledged that Mr. Amri was known to have links to a radical Salafist preacher and had been in their custody pending deportation proceedings after being caught with fake papers. He was freed, even though he was considered potentially dangerous by the authorities

He also appeared on the radar of United States agencies, according to American officials. He had done online research on how to make explosive devices and had communicated with the Islamic State at least once, via Telegram Messenger, said the officials, who spoke on the condition of anonymity because of the investigation. He was also on a United States no-fly list, the officials said on Wednesday evening.