Texas US Senator Ted Cruz has solidified his lead among Republican presidential contenders in the politically crucial state of Iowa, a new poll shows.

The Des Moines Register/Bloomberg Politics poll, out late on Saturday, shows the conservative Cruz with 31 per cent support, 10 points ahead of bombastic billionaire Donald Trump, who has 21 per cent.

Trump, who has a solid lead in national polls among Republicans, quickly tweeted about another survey.

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“New CNN Iowa poll – Trump 33, Cruz 20. Everyone else way down! Don’t trust Des Moines Register poll – biased towards Trump!” he wrote on Twitter, apparently intending to say the Iowa paper was biased against him.

It was unclear what CNN poll Trump was referring to.

Jennifer Jackson of the Des Moines Register said in a video on the paper’s website: “It’s Cruz-mentum. Ted Cruz is crushing it in Iowa.”

The poll follows a December 7 Monmouth University survey showing Cruz for the first time leading the field among voters who intend to take part in the February 1 Iowa caucuses, the first real measure of voter support in the 2016 presidential campaign.

As recently as October, Cruz, 44, had just 10 per cent support in a Monmouth poll.

Trump has complained that the Des Moines Register is biased against him ever since the newspaper’s editorial board called him to drop out of the race in July.

Third in the Des Moines Register/Bloomberg Politics poll is retired neurosurgeon Ben Carson with 13 per cent, followed by Florida Senator Marco Rubio with 10 per cent.

Republican voters seemed to have cooled on Carson – who was leading in Iowa polls in October – likely because of his embarrassing ignorance of foreign affairs.

The telephone poll of 400 Republican voters was taken Monday through Thursday, and has a margin of error of plus or minus 4.9 per cent.

The poll was taken as Trump called on Monday for barring Muslims from entering the United States.

One-time presumed frontrunner Jeb Bush – son of one president and brother to another – has a measly six per cent support, while all the other candidates have less than three per cent support.