Presidential candidate and former Speaker Newt Gingrich (R-Ga.) has apologized to Rep. Paul RyanPaul RyanMellman: First things first? Obama makes healthcare plea in handoff letter to Trump Chamber's 'State of American Business' only about Big Business MORE (R-Wis.) for his criticism of the Medicare reforms in Ryan's 2012 budget proposal.

"The apology centered on the inartful terms," Gingrich spokesman Rick Tyler told The Hill. He said the conversation "went very well."

Ryan and Gingrich exchanged emails Monday and Tuesday before speaking Tuesday afternoon, according to Tyler.

Gingrich has been under fire since referring to Ryan's plan as "right-wing social engineering."

While on a 17-city campaign swing in Iowa, a voter confronted Gingrich, telling the former Speaker: "What you just did to Paul Ryan is unforgivable."

The firestorm began Sunday, when Gingrich distanced himself from Ryan's Medicare plan, which would transform the program into a voucher-based system for Americans under the age of 55.

"I don't think right-wing social engineering is any more desirable than left-wing social engineering," Gingrich said on NBC's "Meet the Press." "I don't think imposing radical change from the right or the left is a very good way for a free society to operate."

Ryan, the chairman of the House Budget Committee, fired back on Monday.

"With allies like that, who needs the left?" Ryan told guest host Raymond Arroyo on conservative talker Laura Ingraham's radio show.

House Majority Leader Eric CantorEric CantorRyan reelected Speaker in near-unanimous GOP vote Financial technology rules are set to change in the Trump era Trump allies warn: No compromise on immigration MORE (R-Va.) also joined the fray, saying Tuesday that Gingrich was guilty of a "tremendous misspeak."

Tyler said Ryan and Gingrich are "old friends" and the former Speaker considers Ryan to be a "tremendous asset to the Republican Party and one of the greatest minds in Congress."

When asked if Gingrich supports Ryan's budget proposal, Tyler said he supports the "framework."

—Michael O'Brien contributed.