Ted Cruz has put himself under self-quarantine after a brief interaction with a person who tested positive for coronavirus, the Texas Republican senator said in a statement on Sunday.

The news came amid reports of increasing nervousness among congressmen and women, most of whom travel regularly between Washington and their districts and many of whom are over the age of 50. Coronavirus is most dangerous to older sufferers and those with underlying health problems.

“Members are very nervous,” NBC News quoted a “senior Democratic leadership aide” as saying. “There’s a lot of concern that members could bring it home.”

The US Centers for Disease Control and Prevention (CDC) says the virus is mainly spread from person to person, in contact within about 6ft. Transmission may occur when “respiratory droplets” produced in coughs or sneezes land in the mouths or noses of nearby people.

At least 21 people have died in the US and there have been more than 500 confirmed cases. According to the World Health Organization, there have been around 106,000 cases around the world, most in China, and around 3,500 deaths.

Cruz said he had come into contact with the individual at the Conservative Political Action Conference (CPAC), at a conference center outside Washington DC.

“Last night, I was informed that 10 days ago at CPAC I briefly interacted with an individual who is currently symptomatic and has tested positive for Covid-19,” Cruz said. “That interaction consisted of a brief conversation and a handshake.”

Cruz said he was not experiencing symptoms and felt “fine and healthy”, adding that medical authorities had told him the odds of transmission “were extremely low”. He will self-quarantine in his home until 14 days have passed since the interaction at CPAC.

On Monday, the Capitol’s attending physician’s office said “several” members of Congress had had contact with the person but “remain in good health”.

In a note to lawmakers, the office said the ill individual had recalled “specific names of people he had contact with during” CPAC.

“Several of these individuals, members of the Congress, were identified and were contacted on the evening of 7 March,” the note said.

Their symptoms were reviewed and the individuals were considered to be at “low risk”, the statement said. It said all the lawmakers the physician’s office was monitoring “remain in good health”.

The Republican representative Paul Gosar announced that he and three members of his senior staff were under self-quarantine after coming in contact with the person who has what the Arizona rightwinger chose to call “Wuhan virus”, after the Chinese city at the center of the outbreak.

Gosar tweeted that he and his staff were showing no symptoms but were “being proactive and cautious”.

The person who attended CPAC, whose name has not been released, is quarantined and under the care of medical professionals in New Jersey.

The CPAC schedule listed three other senators and 12 House members who were scheduled to speak. They included the No 2 House Republican, Steve Scalise of Louisiana; No 3, Liz Cheney of Wyoming; and the congressman Mark Meadows of North Carolina, whom Donald Trump recently named White House chief of staff.

A spokesman for Cheney said she had been told by CPAC she was not exposed to the attendee in question. Nonetheless, Cheney did not attend a party gathering in Maryland over the weekend, after deciding “to limit participation in non-essential gatherings”.

Also on the CPAC schedule was the transportation secretary, Elaine Chao, who is married to the Senate majority leader, Mitch McConnell. David Popp, spokesman for McConnell, said on Sunday evening no changes had been made in the chamber’s schedule. McConnell had spoken with Cruz, Popp said.

The Senate had a vote scheduled on Monday evening and planned to be in session this week. Congress is set for a one-week recess the week of 16 March.

Donald Trump shakes hands with Matt Schlapp. Photograph: Yuri Gripas/Reuters

The American Conservative Union (ACU), the group that organizes CPAC, said in a statement the infected attendee had had no direct contact with Trump, who gave a speech at the conference, or Mike Pence, who was also in attendance.

Matt Schlapp, chairman of the ACU, said he had had contact with the individual early in the conference. Later, Schlapp greeted the president, Pence and several administration officials. A picture shows Schlapp and Trump shaking hands.

Schlapp told the Washington Post he regularly used hand sanitizer during the conference and had not shown symptoms. Experts say hand sanitizers with less than 60% alcohol do not prevent coronavirus transmission.

Asked on Saturday if he was concerned that coronavirus would reach the White House, Trump said: “No, I’m not concerned at all. No, I’m not. We’ve done a great job.”