SEATTLE – Washington Gov. Jay Inslee on Tuesday touted big improvements in distributing the COVID-19 vaccines, but he also urged residents to remain vigilant as new, more contagious variants of the disease spread in the state.

Inslee said more than 36,000 doses were administered in Washington on Sunday and 39,000 on Monday — a big jump from about 16,000 a week earlier, and on the way toward the state’s goal of 45,000 per day.

The number of vaccines actually administered could be even higher, given lags in reporting, but as of Monday more than 500,000 doses had been administered statewide, with four mass vaccination sites due to open this week.

President Joe Biden announced Tuesday the federal government is boosting vaccine supplies to the states by 16% over the next three weeks, giving states more certainty about upcoming deliveries than the one-week notice the Trump administration had been providing.