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.

Nicolás Maduro took the oath before parliament, vowing his third six-year term in office would be a "period of peace".

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.