Mr Abbott is being considered for the role of joint president of the relaunched Board of Trade but his potential appointment is being heavily criticised due to allegations of homophobia and misogyny.
Campaign groups, politicians and celebrities are urging the government to reconsider whether his appointment is appropriate.
Asked during a visit to Solihull about allegations the Australian former prime minister is a sexist, homophobic, misogynist, climate change denier, Mr Johnson said he doesn't agree with everything Mr Abbott may have said, but added how he was elected by a "liberal country".
"I don't, obviously don't agree with those sentiments at all, but then I don't agree with everyone who serves the government in an unpaid capacity on hundreds of boards across the country. "
He added: "What I would say about Tony Abbott is this is a guy who was elected by the people of the great liberal democratic nation of Australia.
"It's an amazing country, it's a freedom-loving country, it's a liberal country. There you go, I think that speaks for itself."
The prime minister said the appointment had not yet been confirmed and an announcment would be made in "due course".
Earlier Transport Secretary Grant Shapps, when asked about allegations against Mr Abbott, said said he isn't an expert on Australian politics, but knows Mr Abbott's sister "is lesbian" and "says her brother went to her wedding and the rest of it".
It is not just within politics that concerns have been raised.
ITV News Political Correspondent Paul Brand has seen a letter sent to the government signed by some of the UK’s most high-profile LGBT campaigners and celebrities. It says Mr Abbott’s views mean he is not fit to be trade envoy.
Mr Abbott has previously said that he feels “a bit threatened” by homosexuality, opposed same-sex marriage and was accused of misogyny by fellow former Australian prime minister Julia Gillard.
Labour has written to the government urging it not to appoint Mr Abbott to the role, saying to do so would be “completely unacceptable” because of his “offensive and outdated” views.
In a letter to International Trade Secretary Liz Truss, shadow women and equalities secretary Marsha de Cordova said: “Tony Abbott’s offensive and outdated views on women are well known, including characterising women as housewives who did the ironing and suggesting that uppermost in two female politicians’ qualities for office were their ‘sex appeal’.
“His views on homosexuality, including his admission that he feels threatened by the LGBT community, and that ‘most people do’, are both dangerous and divisive.”
Ms de Cordova added: “This is yet another example of incompetence from this Government and a failure to respect the diversity of our communities.
“The Labour Party urges the government not to make this appointment and look instead for an expert with views on women and equalities that better reflect our British values.”
Health Secretary Matt Hancock, wearing an NHS badge with the LGBTQ rainbow flag, was questioned on Sky News on Thursday over the suitability of Mr Abbott, who led his nation from 2013 until he was ousted by his own party in 2015.
He said he does not believe that Mr Abbott is homophobic or misogynistic and, when pressed, added: “He’s also an expert in trade.”
Ms de Cordova said Mr Hancock’s comments were “deeply disturbing”.
Labour leader Sir Keir Starmer has said he has “real concerns” about Mr Abbott, adding: “If I was prime minister I wouldn’t appoint him.”
Scotland’s First Minister Nicola Sturgeon said Mr Abbott’s coronavirus views are “deeply offensive and wrong” and he is not fit to be a trade envoy.
Critics have raised concerns at his climate change scepticism and belief that coronavirus restrictions should be lifted.
The Prime Minister’s official spokesman on Thursday insisted that “no decision” on the board’s make-up had been made and declined to comment on the “political debate” surrounding Mr Abbott.