Washington (AFP) - Ted Cruz handily won a presidential nominating contest in Wyoming on Saturday (March 12), adding to his delegate total in his bid to up-end front runner Donald Trump.

The vote in the western US state of Wyoming saw the Texas senator win nine of 12 delegates, while Trump and Florida Senator Marco Rubio each won one delegate.

Meanwhile, at a vote held in Washington, DC, Rubio won 10 of 19 Republican delegates at stake, while Ohio Governor John Kasich walked away with the other nine, leaving none for Trump.

The bombastic real estate mogul maintains a solid lead in national polls and in the overall delegate count, and remains the prohibitive favourite to lock up the Republican nomination.

The caucus results came one day after Trump called off a rally in Chicago amid scenes of violence, which the Republican front runner blamed on protesters, while his rivals point their fingers at his incendiary rhetoric.

In other contests, Hillary Clinton won in the first ever Democratic Party caucus on the Northern Mariana Islands, a US possession deep in the Pacific Ocean.

The former secretary of state won four delegates, while her rival, Vermont Senator Bernie Sanders, won two, US media reported.

Cruz, meanwhile, picked up one delegate in Guam, another US possession in the Pacific, while the island's five other delegates were uncommitted, CNN reported.

On Tuesday (March 15), key elections will be held in five delegate-rich states - Florida, Illinois, Missouri, North Carolina and Ohio.

In the Republican race, a candidate need an absolute majority of 1,237 delegates to lock in the party nomination.