Washington — President Biden announced on Tuesday that his administration is boosting the weekly supply of vaccines to states and territories by 16% next week, and said he hopes to have enough doses to vaccinate 300 million Americans by the end of the summer or early fall.

“This will be one of the most difficult operational challenges we’ve ever undertaken as a nation,” Mr. Biden said about the effort to distribute vaccines. He also said he plans to give governors more advance notice on forthcoming allocations of the shots, adding that the vaccine distribution process established by the Trump administration was “in worse shape than we anticipated.”

Vaccine supply to states, territories and Native American tribes will climb to 10 million doses next week, up from 8.6 million and continue at that rate for the next three weeks. Governors will be given a three-week forecast of their vaccine allocations, giving them more time to prepare vaccine distribution plans.

“We will both increase the supply in the short term by more than 15% and give our state and local partners more certainty about when the deliveries will arrive,” Mr. Biden said. He called vaccine distribution a “wartime effort,” as more than 400,000 Americans have died in one year of the pandemic.

The president claimed there will be enough vaccine to fully vaccinate 300 million Americans “by end of the summer, beginning of the fall.” But he urged Americans to continue to follow coronavirus guidelines, such as wearing a mask.

“Our plan will take time,” Mr. Biden acknowledged. “Despite our best intentions, we’re going to face setbacks.”

Mr. Biden’s announcement came after he predicted on Monday that any American who wants a vaccine will be able to get one by “this spring.”

“I think it’ll be this spring. I think we’ll be able to do that this spring,” Mr. Biden said Monday when a reporter asked him when any American who wants a vaccine should be able to obtain one. “But it’s going to be a logistical challenge that exceeds anything we’ve ever tried in this country. But I think we can do that.”

The new president also increased his hopes for how many doses of the vaccine can be delivered during his first 100 days in office, revising it from 100 million up to 150 million. Dr. Anthony Fauci, now Mr. Biden’s chief medical adviser, said in an interview on CBS’ “Face the Nation” on Sunday that the administration is hoping to exceed its initial goal.

“It’s going to be a challenge,” Fauci said. “I think it was a reasonable goal that was set, we always want to do better than the goal you set, but it is really a floor and not a ceiling.”