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Senator Ted Cruz of Texas brought in more than $12 million for his presidential campaign during the last fund-raising quarter, which ended on September 30, his campaign announced on Thursday.

Mr. Cruz raised substantially less than the amount claimed by Ben Carson, the retired neurosurgeon, whose campaign said last week that he had raised more than $20 million, the most of any Republican who has yet disclosed a fund-raising total for the period. The candidates have until Oct. 15 to file their formal campaign reports with the Federal Election Commission.

But Mr. Cruz’s amount is double what one rival, Senator Marco Rubio of Florida, announced raising over the same period, despite Mr. Rubio’s popularity among some of the Republican Party’s biggest donors. The $12 million figure suggests that Mr. Cruz –— who has battled fiercely with his own party’s leaders –— has amassed a committed following of small donors.

In a statement, Mr. Cruz’s campaign said that more than 6,000 of his contributors had pledged to make recurring donations every month of his campaign, the type of donor that provides important financial sustenance to a candidate as large donors reach the $2,700 limit for the primary election. Those donors, the campaign said, had pledged enough monthly revenue to cover Mr. Cruz’s expenses in the first four primary states, as well as in others where the campaign has set up operations.

“Americans are ready for real change, and I am ready to stand with them to take on the Washington Cartel and return power to the American people,” Mr. Cruz said in the statement. “We have both the financial and organizational resources to compete for the long haul and to take our optimistic message all across the country.”