Two prominent Democratic senators, Elizabeth Warren of Massachusetts and Cory Booker of New Jersey, announced separately on Sunday that they had tested positive with a breakthrough case of the coronavirus.

Both senators disclosed their cases on Sunday, and said they were experiencing mild symptoms after being vaccinated and receiving a booster shot. Ms. Warren said she received the positive result Sunday, while Mr. Booker said his test result came back after he began experiencing symptoms Saturday.

News of the cases came barely a day after the Senate left Washington for the year and ahead of a planned address by President Biden to the nation on Tuesday to respond to the rapid spread of the Omicron variant.

Both senators called on the public to get vaccinated.

“I urge everyone who has not already done so to get the vaccine and the booster as soon as possible — together, we can save lives,” Ms. Warren wrote on Twitter, adding that she had received both a vaccine and a booster shot.

“I’m certain that without them I would be doing much worse,” Mr. Booker said in a statement. “I encourage everyone who is eligible to get vaccinated and boosted.”

President Biden will address Americans on Tuesday as his administration faces questions about how it will respond to the challenges of a pandemic that has persisted well beyond the administration’s expectations.

Mr. Biden “will announce new steps the Administration is taking to help communities in need of assistance,” Jen Psaki, the White House press secretary, wrote on Twitter on Saturday, “while also issuing a stark warning of what the winter will look like for Americans that choose to remain unvaccinated.”

Mr. Biden has both sounded an alarm over Omicron this month while also expressing optimism that the fast-spreading variant would not set back the progress the country has made.

For the unvaccinated, the president said on Thursday, “we are looking at a winter of severe illness and death — if you’re unvaccinated — for themselves, their families, and the hospitals they’ll soon overwhelm. But there’s good news: If you’re vaccinated and you had your booster shot, you’re protected from severe illness and death — period.”