Republican front-runner Donald Trump is putting his precedent-shattering campaign to the test when Iowa voters begin the nationwide process of choosing a new US president.

Polls are showing a tight battle with Ted Cruz that could hinge on turnout and a large bloc of undecided voters.

On the Democratic side, front-runner Hillary Clinton also faces a stiff challenge in Iowa from insurgent Bernie Sanders in the first contest in the state-by-state battle to pick candidates for the November 8 election to succeed President Barack Obama.

Late opinion polls showed Trump, a blunt-spoken billionaire businessman who has never before sought public office, with a small lead on Cruz, a conservative US senator from Texas, while Clinton has a slight edge on Sanders, a US senator from Vermont.