Democrats, seeking to tie abortion restrictions to former President Donald J. Trump and Republicans, again laid the blame for limits on reproductive rights at Mr. Trump’s feet, saying the former president’s statement on Monday calling for abortion restrictions to be decided by states was part of a pattern of “extreme” lawmaking.

In the video he released, Mr. Trump said that states should decide through legislation and make it “the law of the land, and in this case, the law of the state.” A handful of Republicans disagreed, saying he did not go far enough by not endorsing a federal ban or discussing it at all. But Democrats, who have identified reproductive rights as a top campaign issue this year, argue that Mr. Trump effectively did endorse a total ban by leaving the decision to states who will implement one and that, if re-elected, he will enact a total ban on the procedure — something Mr. Trump has not specifically said he would do.

In a blistering 604-word statement, President Biden said via his campaign that Mr. Trump was “responsible for creating the cruelty and the chaos that has enveloped America since the Dobbs decision,” referring to the 2022 Supreme Court ruling in Dobbs v. Jackson, which overturned Roe v. Wade. The president said that his opponent’s abortion stance has created a crisis of his own making. Mr. Trump, he said, is “lying” about the number of Americans who support abortion restrictions and “scrambling” to craft a message around his record.

“Here’s what Donald Trump doesn’t understand: When he ripped away Roe v. Wade, he ripped away a fundamental right for the women of America that the United States Supreme Court had affirmed and reaffirmed for 50 years. As a fundamental right, it didn’t matter where you lived,” Mr. Biden said in the statement.

The president also challenged Mr. Trump’s false statement that Americans widely support restrictions on abortion and said the former president made a “political deal” to appoint Supreme Court justices who would overturn Roe v. Wade in exchange for support from anti-abortion voters.

“Trump admits as much in his statement today,” Mr. Biden said. “Having created the chaos of overturning Roe, he’s trying to say, ‘Oh, never mind. Don’t punish me for that. I just want to win.’”

Democrats running in down-ballot races also pounced on Mr. Trump’s comments. Senator Tammy Baldwin of Wisconsin, facing a tough re-election matchup in November, tied the former president’s comments to that of her Republican opponent, Eric Hovde, saying in a statement that both “will ensure abortion is illegal for women across our state.”

Mr. Hovde has said he supports exceptions for rape, incest and life of the mother. Ben Voelkel, a spokesman for Mr. Hovde, said that Ms. Baldwin was “lying” in her statement and that in addition to supporting exceptions for abortion, Mr. Hovde endorsed having the issue decided at the state level and believes “there should be a period of time at the beginning of a pregnancy for a woman to make a decision.”

In Ohio, the state’s Democratic Party issued a press email arguing that Bernie Moreno, the Republican seeking to unseat Senator Sherrod Brown, a Democrat, would support a national abortion ban with no exceptions. A spokeswoman for Mr. Moreno’s campaign, Reagan McCarthy, pointed to a February debate performance in which Mr. Moreno endorsed a 15-week ban with exceptions for rape, incest and the life of the mother.

President Biden’s campaign held a call with reporters Monday afternoon to discuss the former president’s comments. Shortly after, it released a new advertisement featuring a woman who was denied medical care after having a miscarriage, causing her to develop sepsis and imperiling her chances of becoming pregnant again. The words “Donald Trump did this” flash across the screen after she tearfully shares the contents of a baby box with items she would have used for the baby, named Willow, had she carried her to term.

Democratic groups also weighed in. Jessica Mackler, president of the group Emily’s List, which helps fund candidates who support abortion rights, said that through his comments, Mr. Trump “endorsed every ban that has been introduced across the country.”

“Today’s statement is just a clear sign that Trump understands how toxic his record is to voters,” she said.