Migrant groups have welcomed the changes, but say everyone has a role to play in improving cultural understanding, and seeing the value of migrants beyond their English-language proficiency.
Labor has meanwhile called for an anti-racism strategy.
Three years ago, the federal government proposed changes to the citizenship test which would have required migrants to pass a university-level standard of English language competency test.
Citing national security concerns, the government said the new laws would also require migrants to sign a "values statement" before they could become Australians.
Sustained community pressure meant the proposed bill* was never adopted.
Acting Immigration Minister Alan Tudge says the pandemic has caused the government to reconsider the need to improve social cohesion, particularly the delivery and outcomes of its program providing free English-language tuition for migrants.
"This a billion dollar program, but it presently not having a sufficient impact. It currently provides migrants 510 hours of free language tuition. But on average, people only complete 300 hours of classes, and only 21 per cent leave with a functional level of English. This is just not good enough."
Mr Tudge says estimates show close to a million people across the country lack some English language proficiency, which limits their ability to get a job and integrate in Australian society.
"Those in Australia who don't speak English, only 13 per cent of them are in work. Those who speak English well - that figure is 62 per cent. It is stark. Now this is not to blame anyone whose English language proficiency, but clearly full participation in the community is difficult when there are language barriers. Without any English language skills, migrants are less likely to get a job, less likely to integrate, and less likely to participate in our democracy."
According to census data, the number of people in Australia who said they could not speak English well or at all increased from about 560,000 in 2006 to around 820,000 in 2016.
Mr Tudge says to boost the levels of English language proficiency amongst migrants, the Adult Migrant English Program [[AMEP]] will be changed: the cap on the hours will be scrapped and the time limits removed.
Using a National Press Club speech, he says the new measures will reduce barriers to accessing lessons.
"The current program is mostly classroom-based and doesn't provide the flexibility needed for people working, or with caring responsibilities. And doesn't sufficiently take advantage of the massive opportunities from ed-tech (education technology). In many cases, 510 hours is insufficient, particularly for those whose native language is not a European one, which is many of the major groups of our new migrants today. They may well need a thousand or two thousand hours of classes. This [the changes] means that any permanent resident or citizen who doesn't yet have functional English will be able to attend classes free of charge until they acquire this language capability."
Mohammad Al-Khafaji, the chief executive of FECCA, the main group representing multicultural Australia, says he welcomes the changes.
"Currently, migrants are expected to prioritise a number of different things as part of their settlement journey. One of it is: learning English, but also going out there and finding work and making sure they learn the system and so on. As it was up until today, those priorities usually conflicted, and a lot of migrants could not achieve their level of English. And they had to prioritise finding work over learning English."
He says the pandemic has revealed gaps in the government's engagement with multicultural communities
"In the early stages of the pandemic, FECCA actually called for a multicultural strategy to tackle COVID-19 because we knew there are going to be some gaps and there will be a vacuum created from the lack of in-language material provided to our communities. And I think this is where many communities decided to find information the pandemic in-language, and that is when they resorted to news outside Australia. And we warned about this. But also shows that we need to be better planning ahead of something, before it becomes a problem."
But he warns English-language proficiency being the chief standard of measuring the value of successful migrants.
"English-language requirement is not the only indicator if someone is going to be a good citizen, or not. We have seen post-World War Two who have built business empires, and have been model citizens in Australia and today still have very limited English. So English alone is not an indicator successful settlement and integration in Australia."
A record number of people - more than 200,000 - became Australian citizens in the 2019-20 financial year.
Mr Tudge says from November, administrative changes will be made to the Australian citizenship test to emphasise the importance of loyalty to Australian values like the rule of law, freedom of speech and individual responsibility.
The Australian values statement signed by citizenship applicants will also be updated.
"Australian citizenship is both a privilege and responsibility, and it should be granted to those who support our values, respect our laws and want to contribute to Australia's future. We should ensure that those who come here, and those who settle here clearly understand, and are willing to commit to the shared common values that unite us all as Australians."
Labor's spokesman on Multicultural Affairs, Andrew Giles, says the new changes to the Adult Migrant English Program are welcome, but the implementation will be important.
The Minister is suggesting that there won't be a cap on hours and obviously, we've got to work through the details of what this all means. But it seems to me that additional funding in normal circumstances would be required to meet that aspiration. I am really keen to see the detail of this, to work through it with the experts, the teachers, the providers, and stakeholders to see what can be done within this envelope and whether it is satisfactory."
He says he would like to see an anti-racism strategy form part of the government's policy on social cohesion.
"Certainly we know that racism is on the rise. It was on the rise before the pandemic. And we've seen shocking evidence, including this week in the Senate committee about how racism has increased, particularly towards Asian Australians. And if we don't take it seriously, we're simply not standing up for our multiculturalism. It is fine to assert that Australia is a multiculturalism world leader, but we've got to defend it. And that means defending it from racism."
Mr Tudge also used his National Press Club speech to warn of the threat presented by the growing reach of foreign governments in Australia.
"Despite now being proud Australians some communities are seen by their former home countries as 'their' diaspora - to be harassed or exploited to further the national cause. Some who have criticised their former country are silenced through threats and intimidation - including to family members back in their country of heritage. Others are persuaded to monitor or harass community members who may hold views contrary to those of the governing regimes in their former countries."
He says the government's social cohesion strategy will also include: the launch of a research program to better understand community sentiment towards social cohesion, plans to boost its Community Liaison Officer network to include more officers with dual language skills; and the development of "a broader campaign articulating our national identity".
