Millions of dollars in political advertising from independent groups supporting the Republican presidential candidates are adding another element of unpredictability to an already ­topsy-turvy nomination contest.

A group backing Mitt Romney, known as Restore Our Future, on Thursday launched a $3.1 million advertising campaign that will run in Iowa in the next three weeks. Earlier this week, Make Us Great Again, a group supporting Texas Gov. Rick Perry, reported spending $577,000.

The spending underscores the rapid rise of “super PACs” and their prominence in the 2012 campaign: the $1 million spent so far by independent groups in the GOP primary is four times greater than it was at this point in 2008, according to ad tracking data from Kantar Media.

But all of that independent spending also can mean that voters are getting hit with a lot of different, and sometimes confusing, messages. That stems in part from campaign laws that ban independent groups from coordinating their strategies with the candidates or their campaigns.

“You’re going to have many more players involved,” said Ken Goldstein, president of Kantar’s political ad tracking group. “And when you have more players involved, you can have different strategies and different agendas, even among friends.”

Off message

The ad campaign by Restore Our Future, for example, did not line up neatly with Romney’s evolving campaign message.

On the same day that Romney unleashed a pointed attack on rival Newt Gingrich, the Restore Our Future ad made no mention of the former House speaker, focusing instead on criticizing President Obama as a “community organizer” and “law professor” with no record of creating jobs.

“Mitt Romney turned around dozens of American companies and helped create thousands of jobs,” the ad says, referring to Romney’s time as co-founder of the Bain Capital private equity firm.

The message was similar to the Obama-focused theme that Romney has been sounding throughout his campaign, but far different from the new focus on Gingrich.

Restore Our Future’s treasurer, Charlie Spies, said in a statement that the ad, which also shows background on Romney, highlights the candidate’s “proven track record when it comes to creating jobs, turning an economy around without raising taxes, and taking businesses from bust to boom.”

The group appears to be just one step behind Romney’s campaign. Late Thursday, a 60-second spot attacking Gingrich surfaced on the Internet, but it was quickly removed from YouTube.

Outspending candidates

In some cases, super PACs are spending more on the airwaves than the candidates they are aiming to help.

Jon Huntsman’s campaign hasn’t run any ads, but his super PAC has spent $493,000 on television through the start of this week, according to estimates from Kantar, which don’t include local cable and radio advertisements. The super PAC has reported more than $1 .3 million in total spending to the Federal Election Commission.

Romney’s campaign has spent only $157,000 on ads through Sunday, according to Kantor’s estimate, a rate far lower than the $3.1 million campaign planned by Restore Our Future.

The spending by super PACS has bolstered some candidates who might otherwise have been relegated to obscurity. Our Destiny PAC takes credit for a small uptick in Huntsman’s share of the primary vote in New Hampshire since the group began blanketing the state with ads in mid-November. The super PAC’s pollster, Whit Ayres, said the candidate has doubled his share of the vote to 10 percent, comparable to independent polls.

Restore Our Future’s $3.1 million expenditure takes the ad wars to new heights in what had been a low-spending race to date. The campaigns themselves have spent about one-tenth as much on ads as they did in the frantic 2008 contest, according to Kantar.

Solutions 2012, a pro-Gingrich super PAC that formed a month ago, plans to begin airing ads soon in Iowa to compete with other groups, said Charlie J. Smith, the group’s treasurer.

“Time’s running down to Iowa and we realize that,” Smith said. “Mitt Romney is adjusting his strategy and people around him are bringing out the long knives. It’s a situation where we plan to respond soon.”

Smith said that Solution 2012’s efforts will be focused initially on Iowa, then on the early primary races in New Hampshire, South Carolina and Florida. He declined to say how much the group has raised.

A pro-Obama group called Priorities USA also went up with new advertising this week. The group is spending about $50,000 on a television and Internet ad featuring President Ronald Reagan speaking out in favor of closing tax loopholes on the rich.

Bill Burton, the group’s spokesman and a former White House aide, said “it wasn’t surprising” that Republican groups are vastly outspending Democratic ones, which have had less luck in collecting from rich donors.

Rob Collins, a Republican strategist who ran an interest group attacking Democratic House candidates last year, said super PACs will most likely focus on attack ads and other negative messages, leaving the campaigns to strike a more optimistic tone. Even as the Restore Our Future ad debuted attacking Obama, for example, Romney’s campaign was airing a mostly positive spot focusing on the former Massachusetts governor’s stable family life.

“The super PACs have the luxury of doing a lot of the hard work that campaigns don’t want to have to do,” Collins said. “The message that the candidates say they approve can be a very positive message about the future of the country, and the super PACs can do the harder comparison ads.”