Trump's alleges that Cruz intimidated voters by sending a mailer suggesting that recipients had committed “
voting violations” and assigned them and their neighbors poor grades based on their individual voting history.

Iowa's Secretary of State Paul Pate issued a statement Saturday about the mailers in which he said they misrepresented Iowa election laws and the role of Secretary Pate's office.

"There is no such thing as an election violation related to frequency of voting," Pate writes. "Any insinuation or statement to the contrary is wrong and I believe it is not in keeping in the spirit of the Iowa Caucuses."

Trump also pointed to an incident in which a Cruz staffer told caucus-goers that fellow candidate Ben Carson planned to quit the race, for which Cruz later apologized.

Concerning the mailers, Cruz told the press he would not apologize for using every tool at his disposal to encourage Iowa voters to turn out.

Matt Schultz, the Cruz campaign’s Iowa state chairman and a former Iowa secretary of state, told the New York Times that mailers such as those Trump is lambasting "are a common practice to increase voter turnout".

"Our mailer was modeled after the very successful 2014 mailers that the Republican Party of Iowa distributed to motivate Republican voters to vote, and which helped elect numerous Republican candidates during that cycle," Schultz said.

Ted Cruz won in Iowa with 27.6% of the vote, followed by Donald Trump with 24.3%, Marco Rubio with 23.1%, and Ben Carson with 9.3%.

The candidates will now head to New Hampshire to campaign ahead of that state's primaries.