Even so, the widespread nature of the attempts and the yearlong lag time in notification from the Department of Homeland Security raised concerns among some election officials and lawmakers.

For many states, the calls on Friday were the first official confirmation that they were on the list — even though state election officials across the country have been calling for months for the federal government to share information about any hacks, as have members of Congress.

“It is completely unacceptable that it has taken D.H.S. over a year to inform our office of Russian scanning of our systems, despite our repeated requests for information,” California’s secretary of state, Alex Padilla, a Democrat, said in a statement. “The practice of withholding critical information from elections officials is a detriment to the security of our elections and our democracy.”

Senator Mark Warner of Virginia, the top Democrat on a committee that is investigating Russian meddling in last year’s election, has been pushing the department for months to reveal the identities of the targeted states. He said states need such information in real time so that they can strengthen their cyber defenses.

“We have to do better in the future,” he said.

The Department of Homeland Security said it recognized that state and local officials should be kept informed about cybersecurity risks to election infrastructure.