Missouri congressman Todd Akin uses his new TV ad to ask for "forgiveness"Mr Akin has sparked uproar by claiming women's bodies could prevent pregnancy in cases of "legitimate rape".
He is defying intense pressure from his own party to leave the race, accusing people of over-reacting.
Correspondents say Republicans fear the backlash could sink their bid to win control of the US Senate in November.
Mr Romney said on Monday Mr Akin's remarks were "offensive and wrong", but he had stopped short of urging him to drop out.
"Today, his fellow Missourians urged him to step aside, and I think he should accept their counsel and exit the Senate race," Mr Romney said on Tuesday.
'Taking a stand' Senator Roy Blunt and four former senators from Missouri said earlier in a joint statement that Mr Akin's candidacy did not serve the national interest.
He described the response to his comments as a "little bit of an over-reaction", saying he had mistaken "one word in one sentence on one day".
"By taking this stand, this is going to strengthen our country," the sixth-term lawmaker said. "I hadn't done anything morally or ethically wrong, as sometimes people in politics do."
Last week Mr Akin had a comfortable lead in opinion polls over incumbent Democratic Senator Claire McCaskill in the Midwestern state of Missouri, which has leaned increasingly conservative in recent years.
Then on Sunday, he was asked by a local news station if he would support abortions for women who have been raped.
The 65-year-old lawmaker replied: "It seems to me, from what I understand from doctors, that is really rare.
"If it's a legitimate rape, the female body has ways to try to shut that whole thing down."
The American Congress of Obstetricians and Gynecologists has said Mr Akin's claim "contradicts basic biological truths".
'Gutless little twerp' But even as top conservatives were lambasting the congressman, the Republican Party was reportedly ratifying a call for a constitutional ban on abortion, without any exception for rape or incest.
The position was to be the subject of a vote at the Republican national convention in Tampa, Florida, next week.
In a new campaign advertisement released early on Tuesday, Mr Akin said: "Rape is an evil act. I used the wrong words in the wrong way, and for that I apologise."
But the US Senate's top Republican, Mitch McConnell, said the apology was insufficient.
He said Mr Akin had "made a deeply offensive error at a time when his candidacy carries great consequence for the future of our country".
The National Republican Senatorial Campaign Committee has reportedly told Mr Akin that $5m (£3.2m) in advertising set aside for Missouri would now be spent elsewhere.
The Karl Rove-backed Crossroads organisation also pulled its ads from Missouri.
But Sen McCaskill, whose campaign appears reinvigorated by her Republican challenger's slip-up, wants Mr Akin to stay in the race.
She said Republicans were trying to "kick sand in the face" of their party's voters in Missouri who selected Mr Akin this month as their candidate.
On Monday evening, CNN television host Piers Morgan labelled Mr Akin a "gutless little twerp" for pulling out of an appearance on his show.