Akin said that a woman's body has ways to prevent pregnancy in cases of what he called "legitimate rape."
Romney had previously denounced Akin's comments, but he had not yet urged the Missouri congressman to drop out.
Sen. Mitch McConnell of Kentucky says he's certain Akin truly is sorry for the comments he made. But McConnell says that "when the future of our country is at stake, sorry is not sufficient."
Akin has vowed to stay in the race and has described the calls to leave an "overreaction."
For the second time in two days, Akin went on the radio show hosted by former Republican presidential candidate Mike Huckabee to say he planned to stay in the race, despite constant urging from prominent members of his own party to step aside.
"I guess my question is: Is there a matter of some justice here?" Akin asked. After his original statement, "all of a sudden, overnight, everybody decides, 'Well, Akin can't possibly win.' Well, I don't agree with that."
The race has long been targeted by the GOP as crucial to regaining control of the Senate.
"I hadn't done anything morally or ethically wrong, as sometimes people in politics do," Akin said. "We do a lot of talking, and to get a word in the wrong place, still, that's not a good thing to do, or to hurt anybody that way, it does seem like a little bit of an overreaction."
Hours earlier, he posted a video online in which he apologized again.
But ominous signs were mounting against the six-term legislator from suburban St. Louis, most notably the apparent loss of millions of dollars in campaign advertising money.
The decision to stay or go has some urgency. Missouri election law allows candidates to withdraw 11 weeks before Election Day. That means the deadline to exit the Nov. 6 election is 5 p.m. Tuesday. Otherwise, a court order would be needed to remove a name from the ballot.
The uproar began Sunday, when St. Louis television station KTVI aired an interview in which Akin was asked if he would support abortions for women who have been raped.
"It seems to me, first of all, from what I understand from doctors, that's really rare. If it's a legitimate rape, the female body has ways to try to shut that whole thing down," Akin said.
A day after nudging Akin by suggesting he "take time with his family" to consider his future, McConnell said it was time for Akin to drop out.
North Carolina Sen. Richard Burr and New Hampshire Sen. Kelly Ayotte joined McConnell, as did five patriarchs of the Missouri Republican Party.
Sen. Roy Blunt and four former senators from Missouri John Ashcroft, Kit Bond, Jim Talent and John Danforth issued a joint statement saying they "do not believe it serves the national interest" for Akin to remain in the race.
After his defiant statements on Huckabee's show, Senate Republicans' campaign arm reiterated that it would not support Akin's campaign.
"The stakes in this election are far bigger than any one individual," said Brian Walsh, a spokesman for the National Republican Senatorial Campaign Committee. By staying in the race, Akin "is putting at great risk many of the issues that he and others in the Republican Party are fighting for."
The committee had set aside $5 million for advertising and had other plans for logistical and field support for Akin's campaign before his comments on Sunday.
At least one outside group that has advertised extensively in Missouri, the Karl Rove-backed Crossroads GPS, has also said it was also pulling all of its advertising in Missouri.
Two GOP officials, speaking on the condition of anonymity because they did not want to irritate Akin, said party officials seeking to talk with him were having trouble reaching him Monday night and Tuesday morning.
Akin campaign spokesman Ryan Hite declined Tuesday to reveal Akin's whereabouts but said he was not in his suburban St. Louis campaign office. Hite said the campaign may release information about his public schedule later.
The apology video Akin posted on YouTube early Tuesday was an apparent attempt to claw back some of the lost funding.
"Fact is, rape can lead to pregnancy. The truth is rape has many victims. The mistake I made was in the words I said, not in the heart I hold. I ask for your forgiveness," he said in the video.
Just two weeks ago, Akin was at the top of the political world in Missouri after winning a hotly contested three-way battle with millionaire businessman John Brunner and former state Treasurer Sarah Steelman for the right to challenge McCaskill in the November election. Missouri has grown increasingly conservative in recent years, and McCaskill is seen as vulnerable.
One anti-abortion group expressed support for Akin, while another called on him to step aside.
Missouri Right to Life, which opposes a woman's right to get an abortion even in cases of rape and incest, said Akin's "consistent defense of innocent unborn human life clearly contrasts" with McCaskill's position. But the Christian Defense Coalition called on him to withdraw.
Names are being floated about a possible replacement for Akin. A favorite is Tom Schweich, the state auditor who was courted to run for Senate earlier this year but declined.
Other names mentioned include former Gov. Matt Blunt, the son of Sen. Roy Blunt; two members of Missouri's House delegation, Blaine Luetkemeyer and Jo Ann Emerson; and Akin's two unsuccessful primary opponents, Brunner and Steelman.
Talent, who lost his seat to McCaskill in 2006, said Monday he had been asked to run but declined.
If Akin were to leave, state law gives the Republican state committee two weeks to name a replacement. The new candidate must file within 28 days of Akin's exit.