Biden said his administration is trying to do a "lot of things to accommodate the rights of women" after the ruling, including considering declaring a public health emergency to free up federal resources.
Such a move has been pushed by advocates, but White House officials have questioned both its legality and effectiveness and noted it would almost certainly face legal challenges.
The president said he has asked officials "to look at whether I have the authority to do that and what impact that would have".
Jen Klein, the director of the White House Gender Policy Council, said it "didn't seem like a great option".
"When we looked at the public health emergency, we learned a couple of things: One is that it doesn't free very many resources," she told reporters.
"It's what's in the public health emergency fund, and there's very little money - tens of thousands of dollars in it. So that didn't seem like a great option. And it also doesn't release a significant amount of legal authority. And so that's why we haven't taken that action yet."
— AP