US Republican presidential candidate Newt Gingrich pledged on Monday to remain faithful to his third wife, fighting back against rivals who have raised his past infidelity as an issue. Gingrich made the vow on a day his poll numbers in Iowa declined slightly, although he still has a substantial lead with three weeks to go before Iowa holds the first US presidential nominating contest of the 2012 election year. Appealing for the support of Iowa's influential evangelical Christians, Gingrich promised to uphold the institution of marriage in a letter to Bob Vander Plaats, head of the Family Leader, a powerful evangelical group in Iowa. The fact that Gingrich had to provide written confirmation of his plans to stay faithful to wife Callista suggested that his campaign sees his past infidelity as a potential obstacle. Rival candidate Mitt Romney has run an ad promoting his 42-year marriage to “the same woman,” Ann Romney, and Rick Perry raised the issue in a candidates' debate on Saturday, saying, “If you cheat on your wife, you'll cheat on your business partner.” The former speaker of the U.S. House of Representatives said he would support a federal constitutional amendment that opposes gay marriage by defining marriage as the union of one man and one woman and would back other steps that conservatives say are necessary to preserve marriage. “I also pledge to uphold the institution of marriage through personal fidelity to my spouse and respect for the marital bonds of others,” he wrote. Gingrich, 68, has admitted to cheating on his first and second wives.