New Delhi (CNN) President Donald Trump has privately expressed frustration in recent days about some of the ways his administration is confronting a spreading coronavirus outbreak , according to people familiar with the conversations. Publicly, he has expressed optimism that the virus is "going to go away."

Trump was initially upset that some Americans who tested positive for coronavirus were allowed back into the United States for quarantine instead of remaining in Asia , though on Tuesday he acknowledged it was ultimately the right thing to allow them back into the country.

And he's sided with officials in Alabama who have protested a federal government plan to quarantine some patients in the state, despite federal officials insisting it wouldn't pose a threat to residents.

After both incidents, Trump told people around him he wants to fire those responsible for the decisions, though it doesn't appear anyone has been terminated. Trump hasn't specified particular individuals, venting instead at the broader situation.

The President's frustration reflects a growing sense among Trump administration officials that the coronavirus outbreak will present a greater challenge than previously understood. Trump's instinct is to seal the US off entirely from people who could have the virus, according to people who have spoken to him.

Trump continues to publicly express confidence in his administration's handling of the crisis and optimism that it will be short-lived.

"I think that whole situation will start working out. A lot of talent, a lot of brain power is being put behind it," he said during a news conference on Tuesday in New Delhi.

Privately, however, he's lashed out against decisions made by his team and insisted stricter controls be put in place to prevent those with coronavirus -- even Americans -- from entering the United States.

As first reported in The Washington Post , Trump was upset to learn that 14 Americans who tested positive for coronavirus were allowed to fly back to the United States after spending weeks in quarantine on a cruise ship in Japan. He was initially told they would remain in Asia for further quarantine, and was frustrated he wasn't kept abreast of the decision-making to allow them to return to the US.

Trump complained to multiple White House officials last week that he hadn't been consulted on the decision. But by Tuesday he seemed to agree it was ultimately the right call.

"We did the right thing. If you were out there, if you were an American and you refused to have any help from your country -- these were wonderful people. It wasn't their fault," Trump said in India.

Trump was also upset about preliminary plans to bring coronavirus patients to an Alabama city, telling local officials he was again caught off guard. The Department of Health and Human Services was evaluating the possibility of using a Federal Emergency Management Agency Center for Domestic Preparedness in Anniston, Alabama, as a backup location for Americans infected by the virus.

Alabama Rep. Mike Rogers, a Republican, said he spoke with Trump over the weekend about the plan and said the President was "completely unaware" of the plan and "annoyed that these individuals had even been brought back to continental United States while they were still infected, but assured me he would get to work on trying to stop it."

One of the barometers Trump relies on most, the Dow Industrials, plunged 1,000 points Monday, undercutting Trump's public downplaying of the potential for crisis. Administration officials have been studying for weeks how the virus could affect the American economy, officials said, though their projections have shown only a minor impact.

Trump has heard a somewhat different story from some wealthy donors and business leaders . As early as mid-January, US CEOs were conveying worry to Trump during the World Economic Summit in Davos at how the virus might affect their supply chains and businesses. He mostly shrugged off those concerns, saying the disease was contained to China.

Trump's administration requested $1.25 billion in emergency funding to address the coronavirus, as well as the ability to tap an additional $535 million in emergency funds already appropriated. The White House requested the funds after initially declaring they weren't necessary. Officials have been receiving calls from concerned lawmakers in recent weeks.

One administration official said it's possible there could be further requests once the scale of the outbreak is better understood.

Administration officials are also weighing calling a United Nations meeting to put China on the spot to reveal more information about what they know about the status of the coronavirus, though a final decision doesn't appear to have been made.

It remains to be seen whether Trump himself will scale up public criticism of China for its handling of the crisis. He has avoided direct confrontation of Xi Jinping and instead has praised the Chinese leader's handling of the crisis, even as experts and other administration officials criticize the country's handling of the outbreak.

Trump has also suggested the virus may weaken when weather turns warmer in China, a theory he says was conveyed to him by Xi. But with coronavirus popping up in warmer climates like Italy, that theory is being tested.

"I spoke to President Xi the other day, he is so committed to solving that problem," Trump said in new Delhi. "He is working very hard. He is very capable. The country is very capable and it snuck up on him but I think he's going to do well."