WASHINGTON — If President Trump’s goals in his prime-time address to the nation were to reassure Americans and unify the country in the face of the coronavirus pandemic, it seems safe to say that he achieved neither as of Thursday morning.

The stock markets collapsed another 7 percent in early trading, indicating that investors were hardly assuaged by the president’s 30-day suspension of most foreign travelers coming from Europe or his policy proposals to boost the economy. And his call to “stop the partisanship” ended as soon as he woke up and began issuing partisan attacks on Democrats.

The president’s speech represented a high-stakes gamble at a time of spreading infections and widening fear, with schools, universities, businesses, places of worship and even sports leagues closing their doors and millions of Americans facing economic and social disruption. The decision to address the nation from the Oval Office conveyed a seriousness about the outbreak that the president’s comments until now had not.

His speech itself, however, left much out. While he read the words from the teleprompter about unity, he made no effort to reach out to the opposition to forge a common front. While he talked about travel limits, he misstated what they will be, forcing his administration to clarify them afterward. While he talked about measures to prop up the economy, he did not discuss the troubles with the availability of testing kits or express understanding of the changes in everyday life affecting so many Americans.

“Real leadership in this crisis is going to have to come from governors, from public health officials, and from institutional leaders,” Rod Dreher wrote on The American Conservative’s website. “We saw tonight that even when Trump is trying to be on his best behavior, he just doesn’t have much of a clue about the nature of the crisis, or how it can best be fought.”

Others were willing to give more benefit of the doubt. Rich Lowry, editor of National Review, which had just harshly criticized the president’s “failures of leadership” in handling the outbreak, saw some progress in the speech even as he expressed concern that it would not last.

“The speech represents a marked, welcome improvement in the president’s rhetoric,” he wrote, “but that won’t matter if he goes out and undercuts it tomorrow, and the ultimate verdict on his response will be rendered based on the results.”

The White House rejected the criticism, insisting that the president’s speech had been well received and effective in making clear to Americans that he understands the situation and is determined to react strongly to guard their well being.

“The reaction has been very favorable across the country,” Vice President Mike Pence said on Fox News. “I mean, the American people have seen, once again, that President Trump has no higher priority than the health and safety of the people of this country.”

Mr. Pence was given the assignment of calibrating the president’s message the morning after with a string of television appearances. On NBC’s “Today” show, he acknowledged “that we know there will be thousands more cases of coronavirus in this country,” just days after Mr. Trump promised that it “will go away,” and the vice president acknowledged that it was wrong to dismiss the outbreak as hype.

“Obviously there’s been some irresponsible rhetoric, but the American people should know that President Trump has no higher priority than the health and safety and well-being of the people of this country,” he said, without identifying who was responsible for the irresponsible rhetoric.

Mr. Trump’s call for a suspension of partisanship lasted just nine hours, at least some of which he was presumably asleep. While some of Mr. Trump’s allies and advisers have urged him to stop fighting and assert more national leadership, the president made clear that it does not suit him.

The first of the president’s partisan jabs came before dawn on Thursday morning and had nothing to do with the coronavirus or anything that had happened in the last few days. Instead, he reached back to revive a controversy from a week ago when Senator Chuck Schumer of New York, the Democratic leader, harshly assailed two conservative Supreme Court justices over abortion rights.

Mr. Trump retweeted a March 4 message from Jonathan Turley, a law professor who opposed impeachment, condemning Mr. Schumer: “Schumer’s threat to the Court that ‘you will pay the price’ is a direct attack on the integrity of our courts. I criticized Trump for his reckless comments about the courts. Where is the chorus of condemnation of Schumer? Schumer sounded more like a stalker than a statesman.”

At 6:15 a.m., Mr. Trump went after Speaker Nancy Pelosi of California, complaining about her resistance to his proposal to cut payroll taxes to juice the economy as it reels from fears of the coronavirus but making no mention of the fact that Republican lawmakers have been cool to the idea as well.

“Nancy Pelosi all of a sudden doesn’t like the payroll tax cut, but when Obama proposed it she thought it was a brilliant thing that all of the working families would benefit from because if you get a paycheck, you’re going to take home more money,” he wrote on Twitter, attributing the words to Brian Kilmeade, one of the hosts of “Fox & Friends.”

In his prime-time address to the nation from the Oval Office on Wednesday night, Mr. Trump sounded a different note. “We are all in this together,” he said at the time. “We must put politics aside, stop the partisanship, and unify together as one nation and one family.”

Mr. Trump has spent much of the past couple weeks fighting a partisan battle over his handling of the coronavirus. Democrats have sharply criticized him for making false or misleading statements about the outbreak, not taking it seriously enough, failing to act sooner and undercutting the government’s global health apparatus.

After Wednesday night’s speech, the Department of Homeland Security and White House were forced to clarify two important points: A ban on travelers from Europe would not apply to American citizens or legal permanent residents and it would not impact goods exported to the United States.

Democrats were not the only ones to fault the president or the administration. Thomas P. Bossert, Mr. Trump’s former homeland security adviser, praised the president’s Oval Office address but said on Twitter that “there’s little value to European travel restrictions. Poor use of time & energy.”

Rather than rise above it or reach out to Democrats to provide a unified front, he has aggressively accused them of “politicizing the coronavirus” and “trying to gain political favor by saying a lot of untruths.” At a raucous campaign rally, he called the Democratic criticism “their new hoax,” and was later forced to clarify that he meant only the criticism and was not calling the virus itself a hoax. He later misleadingly blamed President Barack Obama for the slow spread of the test kits, citing a rule that turned out not to be a rule.

When Mr. Trump announced earlier this week that he would meet with congressional leaders to discuss an economic response to the effects of the virus, he meant only Republican leaders. Just last weekend, as the virus spread, the president announced he would skip the annual bipartisan St. Patrick’s Day lunch on Capitol Hill because of his disdain for Ms. Pelosi.

The crossfire indicated how raw the feelings still are following the impeachment battle that ended just last month. Ms. Pelosi lead the House drive to impeach Mr. Trump for abuse of power and obstruction of Congress, and Mr. Schumer was among the most vocal advocates of removing him from office in a Senate trial that nonetheless ended in a near party-line acquittal.

Ms. Pelosi and Mr. Schumer released a joint statement after Mr. Trump’s speech on Wednesday night calling on Republicans to support a bill that included free coronavirus testing, paid emergency leave for workers, a boost in unemployment insurance and other measures.

“We have a public health crisis in this country,” they said, “and the best way to help keep the American people safe and ensure their economic security is for the president to focus on fighting the spread of the coronavirus itself. Alarmingly, the president did not say how the administration will address the lack of coronavirus testing kits throughout the United States.”

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