Daniel Tarullo, a Fed governor who shares Ms. Brainard’s caution, said on Thursday in an interview with Bloomberg that he was still looking for “an affirmative reason to move.”

The government estimated last week that the economy added 38,000 jobs in May, well below market expectations and the pace of hiring so far this year.

The Fed entered the year predicting quarterly rate increases, only to back away from a first increase in March when the economy showed unexpected signs of weakness. Fed officials in recent weeks insisted they were thinking about raising rates in June. Now it seems that too has passed.

Ms. Yellen did not offer a new plan, and that was intentional.

“I know market participants really want to know exactly what’s going to happen,” she said at one point. “There is, as I said about 18 times, no preset plan.”

She devoted much of her speech to the economic uncertainties confronting the Fed. Among them, she numbered the inconsistency of recent economic data and Britain’s coming referendum on whether to remain in the European Union. She said a breakup would be economically disruptive.

“The uncertainties are sizable, and progress toward our goals and, by implication, the appropriate stance of monetary policy will depend on how these uncertainties evolve,” she said.

But reasons for optimism were also on display Monday.

After her speech, Ms. Yellen met with workers at a job-training program in West Philadelphia. During her first year as Fed chairwoman, round tables with workers in Chicago and Chelsea, Mass., brought together many attendees who were struggling to find jobs. The tone of Monday’s round table was notably more upbeat — the seven people who met with Ms. Yellen all had jobs or, if they were in training programs, were optimistic about finding steady work.