President-elect Donald Trump says Venezuela's embattled opposition leader must be protected as President Nicolas Maduro takes the oath of office for a third six-year term.

It is not viable for Venezuelan opposition leader Edmundo Gonzalez to enter the country, his ally Maria Corina Machado said on Friday, shortly after President Nicolas Maduro was sworn in for a third term despite months of controversy over the country's contested July election.

Venezuela opposition leader Maria Corina Machado was detained at a march in Caracas on Thursday in her first public appearance in months and her ally, former presidential candidate Edmundo Gonzalez, demanded she be freed immediately.