"We'll be discussing a possible payroll tax cut or relief, substantial relief, very substantial relief, that's a big number," Trump told reporters on Monday.
He did not provide details but added that a press conference will be held on Tuesday.
Vice President Mike Pence said the administration was consulting Congress on providing paid sick leave to workers, an idea that Democrats already have been trying to advance.
The stepped-up response to the coronavirus came as the number of confirmed cases in the United States hit 605, according to Johns Hopkins University. It said that worldwide, there are 113,584 cases, with 3996 deaths.
The moves also came as stock markets plunged and top health officials urged some people to avoid cruise ships, air travel and big public gatherings.
Meanwhile, the administration was planning to huddle in coming days with executives of the banking, hospital and health insurance industries.
While an across-the-board payroll tax cut has been under discussion, top White House economic adviser Larry Kudlow and others have advocated specific tax credits, loans or direct subsidies to certain industries or hard-hit areas.
A payroll tax cut could encourage consumer spending and help households that might otherwise struggle to make rent and mortgage payments on time or pay medical bills if family members' work hours are reduced during a coronavirus outbreak.
Florida health officials said everyone returning from China, Iran, South Korea and Italy must isolate for 14 days while travellers from other countries affected by the outbreak should monitor their health.
Thirty-four US states and the District of Columbia have reported to the US Centers for Disease Control and Prevention (CDC) infections of the respiratory illness COVID-19 that can lead to pneumonia. Louisiana had the state's first presumed coronavirus case, Governor John Bel Edwards announced on Monday.
As worries over the virus deepened, the Dow fell a record 2000 points when trading opened and the S&P 500 posted its largest single-day percentage drop since December 2008, the depths of the financial crisis. A plunge in oil prices contributed to fears of a looming recession.
Trump, who often points to the stock market as a gauge of his economic record, criticised news media organisations' coverage of the outbreak in a tweet and accused Democrats of hyping the situation "far beyond what the facts would warrant."
The CDC advised colleges and universities to consider asking students studying abroad to return home and cancel or postpone upcoming travel.
Several US universities were either moving to virtual instruction or considering the step and limiting gatherings on their campuses.
Anthony Fauci, head of infectious diseases at the National Institutes of Health, and other health officials say older Americans, especially those with chronic medical concerns, should avoid big social gatherings, cruise ships and airline flights.
As leaders in the US Congress reviewed potential plans for operating amid coronavirus, four Republican lawmakers - Senator Ted Cruz and Representatives Paul Gosar, Doug Collins and Matt Gaetz - announced that they would self-quarantine after coming in contact at a conservative political conference with an attendee who later tested positive for the virus.
Gaetz traveled with Trump aboard Air Force One on Monday.
Trump and Vice President Mike Pence, who is heading the administration's overall response to the crisis, also attended the conference. The White House said there was no indication they came into contact with the infected attendee.
Pence told reporters that he has not been tested for the virus and did not know whether Trump had been.
The coronavirus outbreak, which originated in China late last year, has spread to at least 105 countries and territories.
Italy, which has the second-highest death toll, said it was extending to the rest of the country restrictions on movement imposed on much of its wealthy industrial north in an effort to contain spread of the virus.
The hardest-hit place in the United States has been a nursing home in the Seattle suburb of Kirkland, and Washington state is considering mandatory measures such as banning large gatherings but not necessarily imposing massive quarantines.
The Life Care Center facility has accounted for most of the 18 confirmed coronavirus-related deaths in Washington state.
In California, officials planned to offload 2400 passengers on Monday and Tuesday from the Grand Princess cruise ship, which was barred from returning to San Francisco last week due to a coronavirus outbreak on board.
Most of the passengers will go into quarantine at military bases in the United States, with those requiring immediate medical attention heading to hospitals. The crew of 1100 will be quarantined and treated aboard the ship, unless they are in need of acute care off the vessel.
California has more than 100 confirmed cases, while on the East Coast, cases in New York state rose to 142, up from 105 a day earlier, Governor Andrew Cuomo said on Monday.
