LONDON — Prime Minister Boris Johnson, resisting mounting pressure to fall in line with the radical responses of other European countries to try to curb the coronavirus, stuck to a notably restrained set of measures on Thursday, even as the Trump administration exempted Britain from a trans-Atlantic travel ban.

In a speech and a lengthy news conference that followed, Mr. Johnson and his health and science advisers said the government is asking people with flu-like symptoms to stay at home for seven days and calling on elderly people to avoid cruises and schools to cancel field trips abroad. But Britain will not close its schools and it has yet to ban large public gatherings, like concerts or sports events.

Mr. Johnson’s approach was in marked contrast to those imposed by neighbors like Ireland and Denmark, where the authorities said they would ban mass gatherings and close schools. It raised further questions about why President Trump exempted Britain from the travel ban, but not France or Germany, both of which have gone further than Britain to try to limit the spread of the disease.

Medical officials estimated the number of infected people in the country at between 5,000 and 10,000, some 10 to 20 times the official estimate of 590 cases. These numbers, they warned, will rise rapidly over the coming weeks.