Dr. Anthony S. Fauci, the nation’s top infectious disease specialist, agreed on Monday with his colleague Dr. Deborah Birx that the United States has entered a “new phase” of the coronavirus pandemic, in which the virus is now spreading uncontrolled in some states by asymptomatic people — comments that drew fire from President Trump.

Dr. Fauci said Dr. Birx had been referring to the “inherent community spread” that is occurring in some states, adding: “When you have community spread, it’s much more difficult to get your arms around that and contain it.”

Speaking during a news conference with Gov. Ned Lamont of Connecticut, Dr. Fauci called the community spread “insidious” and noted that it was happening outside of confined spaces like nursing homes and prisons.

In backing up Dr. Birx, the Trump administration’s coronavirus response coordinator, Dr. Fauci indirectly put himself at odds with the president. Earlier on Monday, Mr. Trump had called Dr. Birx “pathetic” on Twitter and suggested that her comments about a “new phase” were an effort to curry favor with Speaker Nancy Pelosi.

At an evening news conference, Mr. Trump appeared to temper his comments about Dr. Birx. “She’s a person I have a lot of respect for,” he said, while defending his administration’s response to the virus.

Former Vice President Joseph R. Biden Jr. responded to Mr. Trump in a tweet on Monday afternoon. “It’s hard to believe this has to be said, but if I’m elected president, I’ll spend my Monday mornings working with our nation’s top experts to control this virus — not insulting them on Twitter,” Mr. Biden said.

But other Republicans piled on. “Dr. Birx, like Dr. Fauci, has been wrong much more than she has been right on COVID-19, & their destructive prescriptions have led to the devastation of countless American lives,” Representative Andy Biggs, Republican of Arizona, wrote on Twitter.

Dr. Birx had warned during an appearance on the CNN program “State of the Union” on Sunday that the United States was entering a “new phase” in its fight against the pandemic, and that rural communities would not be spared. “It is extraordinarily widespread,” she said.

On Monday morning, shortly after Mr. Trump tweeted about her, Dr. Birx told governors on a weekly briefing call that a lack of masks at large gatherings in homes was “a critical issue,” pointing to spikes in many Southern states.

Mr. Trump has also criticized Dr. Fauci, despite his claims that the two have a “very good relationship.” In a tweet on Saturday responding to news reports that Dr. Fauci had linked the recent surge in cases to inadequate lockdowns, Mr. Trump tweeted: “Wrong!”

In a livestreamed conversation on Monday with Dr. Howard Bauchner, the editor in chief of The Journal of the American Medical Association, Dr. Fauci said that as communities around the country struggle to decide whether and how to reopen schools, scientists “really need to be humble.”

There are significant gaps in knowledge about how likely children are to contract the coronavirus, become ill and transmit the disease, Dr. Fauci said. A recent study found that young children carried high levels of the virus in their noses and throats, for example, but did not prove they were contagious.

Dr. Fauci said he hoped some questions about the risks to children and their role in transmission would be answered by a new government study that involves 6,000 people and seeks to find the rate of infection in children and their families.