The New York senator's total included $4.2 million raised through the Internet. The campaign did not specify how much of the $36 million was available only for the primary election and how much could be used just in the general election, if she were the party's nominee.
The amount outdistanced past presidential election records and set a high bar by which to measure the fundraising abilities of her chief rivals.
The fundraising deadline for the January through March period was Saturday, with financial reports due April 15.
Former Senator John Edwards reported his initial campaign cash drive at $14 million. That's double what the North Carolina Democrat raised in the same time period in his last run for the White House.
Experts have predicted this will be the first $1 billion presidential contest, reports CBS News correspondent Joie Chen. Outrageous as it sounds, it looks like they're right.
Nineteen moths ahead of election day, candidates aren't just running for president, adds Chen. They are running for the money.
Clinton, for example, hit three fundraisers in the 24 hours before Saturday's midnight deadline. Former New York Mayor Rudy Giuliani pressed donor flesh just about every day for the last two weeks.
Republican Phil Gramm of Texas and Democrat Al Gore of Tennessee hold the high-water mark for first quarter receipts: $8.7 million for Gramm in 1995 and $8.9 million for Gore in 1995. Gramm dropped out before New Hampshire held that election's first primary.
Clinton's campaign manager, Patty Solis Doyle, told reporters she was "completely overwhelmed and grateful" by the support.
By not breaking down the amount available for the primaries, the Clinton camp made it impossible to make clear comparisons to past campaigns.
Most of the top tier candidates in the Republican and Democratic fields for 2008 are raising money for the primaries and the general election. The general election money can only be spent if the candidate wins the nomination.
Sen. Barack Obama, D-Ill., also has raised money aggressively and aides said he had more than 83,000 donors. Clinton's supporters had fretted in recent weeks that Obama could surpass her in fundraising.
Obama, in an interview with The Associated Press on Sunday, was coy.
"I think we'll do well," Obama said. "I think that we should meet people's expectations, more importantly I think we will have raised enough money to make sure we can compete for the next quarter and beyond. I think we'll do pretty well."
No Republican presidential candidates had released fundraising totals on Sunday.
For the first time since the post-Watergate era changes to campaign finance laws, candidates are considering bypassing both the primary and the general election public financing system for presidential races. Several of the top candidates are raising both primary and general election money, artificially inflating their receipts.
Candidates cannot touch their general election money and must return it to donors if they do not win the nomination.
The Federal Election Commission ruled recently that candidates could also collect general election money now and still accept public financing later, provided they returned the money they raised. The opinion came at the request of Obama, who then said he would finance his general election campaign if his Republican rival did as well.
Sen. John McCain, R-Ariz., issued a similar challenge.
The first quarter totals are one gauge of a campaign's strength. Compared with previous elections, attention to fundraising during the first three months of this year has been especially acute because the leading candidates have decided to forgo public financing for the primaries.