LONDON — After an inept start to campaigning in Britain’s general election and a pause following the Manchester bombing, Prime Minister Theresa May on Monday navigated a television debate and interview without sustaining further political damage, yet without banishing doubts about her leadership that were raised by a significant policy reversal last week.

During 90 minutes of questions put separately to Mrs. May and to the leader of the main opposition Labour Party, Jeremy Corbyn, the prime minister appeared less comfortable under hard questioning, but she did not crack.

Mr. Corbyn did well, keeping his cool and sense of humor, but had difficulty explaining away his past sympathies for groups like Hamas and Sinn Fein while trying to paint a picture of a better future with more money for nearly every social service coming from higher taxes on corporations and those earning more than 80,000 pounds a year, or about $103,000.

But neither politician emerged as a clear victor. And while the opinion polls are narrowing, Mrs. May’s Conservative Party still seems to hold a significant — though single-digit — lead over Labour for the election on June 8.