President Trump spoke after a trip where he spent time with two congressmen who were exposed to a person infected with the virus. His new chief of staff has also quarantined himself.

President Trump moved on Monday to address the economic effects of the widening coronavirus crisis by announcing that he would work with Congress on tax cuts and other measures after the worst stock market drop in more than a decade.

The president, who played down the virus threat earlier in the day, made an unscheduled evening appearance in the White House briefing room after two Republican members of Congress who have spent time with him in recent days, including one who just rode with him on Air Force One, put themselves into quarantine following exposure to the virus.

Also putting himself into isolation was Mark Meadows, the president’s newly designated White House chief of staff. Mr. Meadows, who was named to the role only on Friday and is stepping down from his House seat representing North Carolina, came into contact with the same infected attendee as the other two congressmen at a recent conservative political conference. While he tested negative for the coronavirus, his office said, he would remain quarantined until Wednesday out of caution.

While none of the three men have displayed symptoms, the threat of the virus coming so close to the president represented a new stage of the outbreak even as organizations across the country restricted travel and canceled gatherings. Mr. Trump made no mention of his own contacts with the affected lawmakers, but his spokeswoman, Stephanie Grisham, later said the president would not be tested “because he has neither had prolonged close contact” with confirmed patients “nor does he have any symptoms.”

But clearly unsettled by the plunging markets and the potential effect on his re-election prospects, Mr. Trump offered an economic response without any new health measures.

Speaking with reporters, he said he would meet on Tuesday with Republican congressional leaders to discuss a “very substantial” payroll tax cut and legislation to protect hourly wage earners who miss work because of the virus. He said he would also explore expanding loans by the Small Business Administration. He did not provide any details.