On NBC News' Meet The Press Sunday, U.S. Republican presidential candidate Sen. Ted Cruz refused to throw Paul Ryan a conservative bone. Pictured: Cruz was introduced at the North Texas Presidential Forum hosted by the Faith & Freedom Coalition and Prestonwood Baptist Church in Plano, Texas, Oct. 18, 2015. Reuters

Sen. Ted Cruz, R-Texas, an influential right-wing lawmaker running for president, refused to call Rep. Paul Ryan, R-Wis., a "true conservative" Sunday when he was asked about the ongoing race for Speaker of the House that has highlighted the rift among House Republicans. Ryan, who has not made a formal decision as to whether or not he will run for the speaker spot, is widely seen as one of the best chances Republicans have for rallying support between the more moderate House Republicans and the several dozen hard-line conservative members who are the source of all the turmoil.

"I like Paul Ryan. He’s a friend of mine. This is obviously a question that is wrapped up in the Speaker of the House deliberations," Cruz told NBC News' Meet the Press host Chuck Todd. Cruz refused to give an opinion that could influence the speaker race. When pressed, he doubled down and added that he thinks syndicated conservative Radio Host Mark Levin is a "true conservative." Levin has recently said he does not think Ryan is in that category.

Rep. Paul Ryan (WI) - Profile | InsideGov

While Cruz himself is not a member of the House of Representatives and therefore can't vote for who will pick up the gavel, he does wield considerable influence in the House Freedom Caucus, a group of roughly 40 lawmakers that has tied up legislation in the House that they don't see as being conservative enough. The task before House Republicans, as they look ahead to picking a new speaker to replace soon-to-be-retired Rep. John Boehner, is to find a leader who can strike a balance between the two groups and move legislation.

Boehner announced in September that he would step down from both his position as speaker and from his congressional seat by the end of October. The announcement came as a surprise for many, and the natural successor to the post, House Majority Leader Kevin McCarthy, R-Calif., ultimately withdrew before an inter-conference vote could be held behind closed doors. McCarthy's decision to step back from the race quickly sparked talks that Ryan could jump in and win the spot. Ryan, who is currently the chairman of the House Ways and Means committee, which he reportedly likes quite a bit, has indicated that he's open to running but doesn't plan on negotiating with ultra-conservative members for a job that he didn't want in the first place.

Cruz finds himself in fourth place in the Republican primary field, according to averages of polling by Real Clear Politics. Of the candidates who have held elected public office, he is the second-most popular candidate in the field.