(CNN) President Donald Trump on Wednesday placed Vice President Mike Pence in charge of the US government response to the novel coronavirus , amid growing criticism of the White House's handling of the outbreak.

At a wide-ranging White House news conference, the President defended the White House's response , stressing the administration's ongoing efforts and resources devoted to combating the virus.

"Because of all we've done, the risk to the American people remains very low," Trump said.

The President did not close the door to Senate Democrats' call for more than $8 billion in emergency funding for anti-coronavirus efforts, despite Democrats' dramatic jump from the $2.5 billion in total funding proposed by the White House.

"We'll spend whatever is appropriate. Hopefully, we won't have to spend so much because we really think that we've done a great job in keeping it down to a minimum," Trump said.

The President did not announce any new travel restrictions during the news conference, saying that "right now it's not the right time" for restrictions on other countries, including South Korea and Italy, which have had a large number of coronavirus cases.

As CNN previously reported , Trump had been privately lashing out at officials for coronavirus-related decisions. His instinct has been to seal off the US from those testing positive, even Americans, though he acknowledged at a news conference in India that allowing them back into the US was the right thing to do.

He also told reporters Wednesday that the US was obliged to repatriate the infected American citizens who were aboard the Diamond Princess cruise ship

"We could have left them and that would have been very bad," Trump said.

On Tuesday, one of the top officials at the Centers for Disease Control and Prevention had warned Americans that health experts foresee the coronavirus, which has killed thousands abroad, spreading in the US.

"We expect we will see community spread in this country," said Dr. Nancy Messonnier, director of the CDC's National Center for Immunization and Respiratory Diseases. "It's not so much a question of if this will happen anymore, but rather more a question of exactly when this will happen and how many people in this country will have severe illness."

But Trump appeared to push back on the CDC's assessment, saying Wednesday that he does not believe that community spread in the US is inevitable.

The President told CNN Chief Medical Correspondent Dr. Sanjay Gupta at the briefing that he's not worried about the spread of the virus in the US.

"No, because we're ready for it," Trump responded. "It is what it is. We're ready for it. We're really prepared. We have, as I said, we have the greatest people in the world. We're very ready for it."

The President said that most of the Americans who have been diagnosed with the virus in the US are doing well.

"Of the 15 people ... eight of them have returned to their homes, to stay at their homes until they're fully recovered. One is in the hospital. And five have fully recovered. And one we think is in pretty good shape," Trump said, but later added, "One is pretty sick but hopefully will recover."

The President returned from India to see his administration on the defensive over its handling of the coronavirus, as Cabinet officials were grilled in Congress and Democrats panned the White House's budget request to fight the virus.

The stock market decline especially has exacerbated Trump's rising concerns over how to stem the outbreak of the coronavirus even as he has publicly declared the virus to be "very much under control in the USA," multiple people tell CNN.

But investors are growing concerned about the economic impact of the virus, as is the President, whose reelection campaign is banking on a strong economy.

The President suggested at the news conference on Wednesday that Tuesday night's Democratic debate in South Carolina was part of the cause of the stock market decline -- even though it took place after the market's dip.

"I think you can add quite a bit of sell-off to what they're saying," Trump said. "I really believe that's a factor."

Trump has been publicly downplaying the novel coronavirus' effects, because he thinks doing otherwise could cause further panic in the markets -- and he's been frustrated with officials issuing warnings about the unknowns of the virus's spread. Trump's son-in-law, Jared Kushner, is one aide who encouraged Trump to downplay the latest developments, at least publicly, one person says.

Unhappy with administration's response

The appointment of Pence came after the White House denied it was considering appointing a czar to oversee the administration's response outbreak.

Trump said Pence would not be a "czar," but stressed the vice president will be coordinating the efforts.

"Mike will be working with the professionals, doctors and everybody else that is working. The team is brilliant. I spent a lot of time with the team the last couple weeks," the President said. "But they are brilliant and we're doing really well and Mike is going to be in charge and Mike will report back to me. But he has a certain talent for this."

According to administration sources, Trump has been displeased with Health and Human Services Secretary Alex Azar -- for failing to keep him updated on crucial decisions concerning the virus.

Lawmakers have also called on Trump to appoint someone to oversee the response, which came up during a clash over the administration's request for more coronavirus funding. Some White House officials accused HHS of requesting disproportionate amounts of money to cover up what one official described as Azar's "mismanagement."

Standing beside Trump and Pence at the end of the news conference, Azar asserted that he's still the chairman of the coronavirus task force and added that he was "delighted" to learn the vice president would be leading the administration on the issue.

Travel restrictions under consideration

Earlier this month, the US began implementing travel restrictions on foreign nationals who had visited China and US citizens who have been near the epicenter of the coronavirus outbreak in China's Hubei province. Before Trump announced the China restrictions, there was a debate inside the White House about the logistics of applying such a ban.

And behind the scenes, Trump is pushing for more travel restrictions on countries the virus is spreading to, administration officials tell CNN, but so far no decisions have been made.

Administration officials have been privately weighing imposing additional travel bans, a senior administration official and sources close to the White House said.

The administration increased the travel advisory warning for Japan and South Korea earlier this week, so those two countries would be likely targets for increased travel restrictions.

There have been more than 80,000 cases of coronavirus globally and the death toll has risen to more than 2,700, the majority in mainland China.

The US has 60 confirmed cases, US health officials said Tuesday, a number that is expected to grow.

Despite the spread of the virus, World Health Organization officials are not yet calling this a pandemic , though they're close.

In January, the WHO declared the outbreak a "public health emergency of international concern."

This story has been updated with additional comments from President Trump's news conference on the novel coronavirus.