• President Joe Biden set two new vaccination goals for July 4: Getting 70% of U.S. adults to receive at least one shot and having 160 million adults fully vaccinated.
• The country would hit those goals by mid-June if the current vaccination rate held steady between now and then, but the pace of daily inoculations has been falling, down 35% from peak levels a few weeks ago.
• U.S. case counts fell further Tuesday to an average of 48,100 per day over the past week.

President Joe Biden on Tuesday said the United States would soon be entering a "new phase" of the country's vaccination campaign once the most eager Americans have received a shot.

Biden set two new goals for July 4: Getting 70% of U.S. adults to receive at least one dose of a Covid vaccine and having 160 million adults fully vaccinated.

The country would hit those goals by mid-June if the current vaccination rate held steady between now and then, but the pace of daily inoculations has been falling for weeks, down 35% from peak levels a few weeks ago.

In response, the government is making changes to its vaccination strategy. Covid vaccines that go unused or unwanted by some states will now be redistributed elsewhere. Biden also announced efforts to make getting a vaccine easier, such as directing federal pharmacy partners to provide walk-in hours and shipping new allocations of vaccine to rural health clinics.

U.S. case counts fell further Tuesday to an average of 48,100 per day over the past week, according to Johns Hopkins University data.

U.S. vaccine shots administered

Centers for Disease Control and Prevention data show the U.S. is reporting an average of 2.2 million daily vaccinations over the past week, down from a peak of 3.4 million on April 13.

The pace of individuals receiving their first vaccine doses has fallen even more steeply, indicating that there are fewer people initiating a vaccination program.

U.S. share of the population vaccinated

About 56% of those aged 18 and older have received at least one dose of a Covid vaccine, with nearly 41% fully vaccinated.

While Biden's 70% target is for the country as a whole, a few states have already crossed the threshold. More than 70% of adults have received at least one vaccine dose in New Hampshire, Massachusetts, and Vermont.

U.S. Covid cases

The rate of daily new infections fell below 50,000 per day over the weekend and continues to decline, according to Hopkins data, as the latest seven-day average stands at 48,100 cases per day.

Average daily case counts have fallen by at least 5% in more than half of U.S. states over the past week.

U.S. Covid deaths

The U.S. has reported an average of more than 700 daily Covid deaths over the past seven days, Hopkins data shows.

CNBC's Berkeley Lovelace Jr. and Kevin Breuninger contributed reporting.