WASHINGTON — Missouri Representative Todd Akin raised about $1.6 million for his Senate bid in the months after Republican officials sought to distance themselves from him for his comments on ‘‘legitimate rape,’’ according to his filings with the Federal Election Commission.

Akin’s third-quarter report, which includes donations from mid-July through the end of September, showed he has about $553,000 in cash on hand. His opponent — Senator Claire ­McCaskill, a Democrat — raised $5.8 million in the same time period, with about $2.1 million on hand. That ­indicates Akin is likely to be outspent in the race.