Ms. Gillibrand transferred $9.6 million from her Senate account to her presidential campaign, and the campaign ended the quarter with $10.2 million in cash on hand, Ms. Kelly said.

In a memo on Sunday, Ms. Gillibrand’s campaign suggested that her fund-raising had been hampered by a continuing backlash to her decision in 2017 to call for the resignation of a fellow Democratic senator, Al Franken of Minnesota, over sexual harassment allegations.

“There’s no question that the first quarter was adversely impacted by certain establishment donors — and many online — who continue to punish Kirsten for standing up for her values and for women,” the memo, which was obtained by The New York Times, said.

Monday is the deadline for candidates to report their first-quarter fund-raising to the Federal Election Commission, and the announcement by Ms. Gillibrand’s campaign came after many of her rivals had already revealed their fund-raising totals.

Ms. Gillibrand’s total for the first quarter ranks, at best, eighth among 2020 Democrats. Senator Bernie Sanders of Vermont leads the candidates with $18.2 million raised in the quarter, followed by Senator Kamala Harris of California with $12 million, former Representative Beto O’Rourke of Texas with $9.4 million and Pete Buttigieg, the mayor of South Bend, Ind., with more than $7 million, according to figures announced by the campaigns.