Tea Party favorite Ted Cruz is pulling ahead in the crucial first-in-the nation caucus state of Iowa, where the Texas senator now holds a 9-percentage point lead over national GOP front-runner Donald Trump, a new poll revealed.

But according to the CBS News 2015 Battleground Tracker, the real estate tycoon still holds considerable leads in New Hampshire and South Carolina, the sites of two other key primary races, the network reported.

In Iowa, where caucusgoers are set to kick off the 2016 electoral calendar in February, Cruz now logs 40 percent support among Republican-leaning voters, the survey revealed. The Texan is trailed by Trump at 31 percent and Florida Sen. Marco Rubio at 12 percent. All other GOP presidential hopefuls, meanwhile, come in at single digits in the Hawkeye State, according to CBS News.

In New Hampshire, meanwhile, Trump maintains a commanding lead of 32 percent, while Cruz, Rubio and New Jersey Gov. Chris Christie come in at a statistical tie of 14, 13 and 11 percent, respectively. In South Carolina, finally, the former "Apprentice" star equally polls at 32 percent, but Cruz at 23 percent is well ahead of Rubio at 12 percent in the Palmetto State.

The poll highlights the differences between both states particularly concerning "jobs and the economy" and "faith and values." People in Iowa, according to the poll, place more importance in faith (21 percent) than the economy (18 percent) than New Hampshire. Twenty-eight percent of Republicans in New Hampshire placed more emphasis in the economy than faith, with only 6 percent viewing it as important.

However, Republicans in both states placed a much higher importance on national security. In Iowa, 61 percent saw it as an important topic while in New Hampshire it was 66 percent.

The Cruz campaign has not made any comments on its candidate's recovery in Iowa, but the campaign's Twitter account did retweet an article from Breitbart highlighting the increase. Before a campaign rally in Mechanicsville, Virginia, on Friday, the senator himself told reporters that his uptick was due to conservatives uniting behind him.

"I'll tell you, the enthusiasm that we are seeing all across the country is really breathtaking," he boasted.

Trump, for his part, remained uncharacteristically mom on the new survey, instead focusing on a poll in Illinois, which is not considered a critical primary state in the race for the Republican nomination.

"Great poll out of Illinois! Thank you!" the 69-year-old noted, nevertheless, on social media.