ABC News' Michael Falcone reports:

When the Michigan Republican Party appeared to bend party rules in order to award one more delegate to Mitt Romney after his win in the state's primary last month, Rick Santorum's campaign cried foul.

Santorum aides accused Romney of "backroom dealing," and trying to "rig the outcome of an election."

Now, Santorum campaign officials say Republican National Committee Chairman Reince Priebus has offered personal assurances to a lawyer for Santorum that the RNC would look into the matter.

Priebus, according to sources on Santorum's team, recently told Santorum campaign counsel Cleta Mitchell, a prominent Washington lawyer, that he would take action on a letter she sent to the RNC earlier this month requesting an "investigation" into what led a six-member committee of Michigan GOP officials to award 16 delegates to Romney and 14 to Rick Santorum after the race appeared to end in a delegate tie.

"It's our understanding that a review is taking place on that delegate," Santorum strategist John Brabender said in an interview with ABC News "We feel that Romney is gaming the system. When we think they're doing to that we're going to expose it."

Romney won the popular vote in the February 28 Michigan primary, 41 percent to 38 percent for Santorum.

Officials at the RNC, however, say a formal review will have to wait until the week before the Republican National Convention when the party's Committee on Contests will meet to consider delegate disputes.

Mitchell's March 2 letter, sent on behalf of the Santorum campaign, asks that the Michigan matter "be referred to the RNC's General Counsel's office for an immediate review and formal investigation."

But the RNC emphasized that, in this case, no such review process exists.

Since the Michigan incident, tensions between the Romney and Santorum campaigns over the delegate math have intensified. According to the latest ABC News tally, Romney has won 521 delegates compared to 253 for Santorum, 136 for Gingrich and 50 for Ron Paul. 1,144 delegates are needed to clinch the nomination.

Santorum faces a daunting challenge to catch up with Romney in the remaining primaries and, his campaign appears to be adopting a leave-no-delegate-behind strategy. It rests on a possible re-allocation of delegates in states like Florida and Arizona, which the Santorum campaign argues should have been proportional not winner-take-all.

Campaigning in Missouri over the weekend, Santorum hinted that his campaign would soon be unveiling "some new delegate math" that he said, "shows this race is a lot different than what the consensus is."

At issue in Michigan the allocation of the state's two at-large delegates. Before the primary, Michigan GOP officials said the party's own rules stipulated that the two would be split between candidates who received more than 15 percent of the vote. That would have left Romney with one and Santorum with the other, resulting in a 15 to 15 delegate tie.

That became the prevailing interpretation until two days after the primary when the state party stepped in to say that an early February decision by the party's Credentials Committee actually provided for a winner-take-all allocation of the at-large delegates.

Until then, Michigan GOP Chairman Bobby Schostak told reporters that the two at-large delegates would be allocated proportionally, and the party echoed those rules in a memo circulated to all of the presidential campaigns.

ABC's Arlette Saenz contributed reporting from Missouri.