"Let's be clear: the day we got here, 4000 people a day were dying and one percent of Americans were vaccinated. Today, deaths are down 75 percent, and almost 200 million Americans are fully vax'ed," he said in a tweet. "We still have a LOT of work to do.
"But if anyone wants to have a debate about COVID, bring it on," he added.
Klain's comments were in response to a New York Times report on Republicans who have criticized Biden's handling of the pandemic. Republicans have hammered the president over the fact that the pandemic has continued despite Biden promising on the campaign trail to "shut down" the virus if elected.
House Minority Leader Kevin McCarthy blasted the Biden administration during his record-long floor speech last week.
"I took President Biden at his word; I took him at his word when he said he was going to get COVID under control," McCarthy said. "Unfortunately, more Americans have died this year than last year under COVID."
The majority of deaths have been among unvaccinated Americans.
Roughly 70% of the American population has received at least one shot of a vaccine, and those figures could rise under policies enacted by the Biden administration.
Biden has pushed for all government employees, military service members, contractors and companies with 100 employees or more to enforce vaccine mandates, policies Republicans have ardently fought against.
The Centers for Disease Control and Prevention (CDC) is now encouraging people to not only get vaccinated but to get booster shots ahead of the winter months.
Vaccinations appeared to significantly help lower infection rates in the spring and into the early summer months.
But the spread of the delta variant, a newer and deadlier strain of the coronavirus, prompted caseloads to spike to rates not seen since before the vaccine became widely available.
On Monday, the CDC confirmed more than 162,000 new cases of the virus were reported during a seven-day rolling average, including 1,200 deaths.
While the U.S. is again seeing higher rates of infection, the number of related deaths remains on a downward trend since the delta virus took hold in August.