The 67-year-old president said he would lead the country "with the full commitment required to deliver real solutions to every corner of our beloved Honduras."
The inauguration was held on Tuesday in an austere, simple ceremony at Congress without the presence of dignitaries from other nations, though representatives of various countries attended through the diplomatic corps and international organisations.
Asfura's rise to power was marked with controversy after US President Donald Trump threw his support behind the Honduran conservative in the lead-up to the election.
Competitors called the elections fraudulent as vote counts dragged on for weeks and Asfura won by less than a one per cent lead.
Honduran authorities said Asfura won with 40.27 per cent of the vote, just ahead of conservative competitor Salvador Nasralla with 39.53 per cent. Nasralla maintains he is the rightful president.
Asfura on Tuesday said he would shrink the size of the state to improve efficiency and direct resources to those most in need.
He pledged to "confront insecurity head-on" as gang violence continues to ravage the Central American nation, and said he would invest in health care and education. He also emphasised the need to attract investment to generate jobs and to boost infrastructure so there is greater connectivity among municipalities.
Asfura served two terms as mayor of Tegucigalpa from 2014 to 2022. He previously served as secretary of the Honduran Social Investment Fund during the administration of Porfirio Lobo Sosa from 2010 to 2014.
The outcome of the complicated election is part of a broader shift to the right taking place in Latin America and came after Chile elected far-right politician José Antonio Kast as president.
