"Our country is in trouble, our economy is stagnant, our society is fragmenting, our security is in peril," Mr Abbott told ABC Radio on Monday.
The comment came after he was elected unopposed to his role on Friday, following a meeting of the Liberal Party's federal council.
"Part of the Australian dream has always been to be able to get ahead and keep most of what you have created for yourself and not have it confiscated by an extortionate government, and that's what Anthony Albanese is now doing," he said.
"History proves that it's the Liberal-National coalition that is the best and strongest alternative government."
Mr Abbott's role is primarily to guide the party and ensure it runs smoothly ahead of the expected 2028 federal election. Â
Mr Abbott's popularity has been proven by agreement from party members but political analysts suggested his vocalness could cause trouble for current Opposition Leader Angus Taylor.
Mr Taylor, a mentee of the former party leader, backed Mr Abbott as party president.
Though it is usually a behind-the-scenes position, Mr Abbott has so far been public in the direction the party should go.
"The party president is the organisational leader, not the political leader, but I don't think there's ever been a party president who's taken a vow of silence, and I'm certainly not going to start," he said.
"My presence in this senior role will demonstrate to people who might have been sceptical about the Liberal Party is fair dinkum about cutting back mass migration, fair dinkum about scrapping taxes, because my government was actually very good at that.
"My presence, I think, is an indicator that the Liberal Party hasn't forgotten how to be a very, very good government."
Shadow Treasurer Tim Wilson said Mr Abbott's role as federal president was an administrative one.
"It's the job of the parliamentary party to make the case for policy, not the job of the federal president," he told ABC's RN.
Mr Wilson said he was "absolutely confident" Mr Abbott understood that difference.
"Most people couldn't tell you who the federal presidents are of political parties."
Opposition frontbencher Andrew Hastie said Mr Abbott's appointment would give the Liberals a boost.
"Morale is important and I think Tony Abbott will bring a boost to morale given his stature as a former prime minister but also as a leader in the centre-right movement, so he was elected unanimously," he told ABC TV.
"We need leadership at the lay party level and that is what Tony Abbott's going to bring."
Mr Abbott's comments have been backed by Liberal MPs, including youth spokeswoman Angie Bell
"Most young Australians are doing everything they can to get ahead; studying, working, building careers, starting businesses and trying to save for a home - the last thing they need is politicians writing them off as lazy," she said in a statement.
