While there was no “causal connection” between poor English and extremism, language lessons would make communities “more resilient”, the PM said.
They would also help tackle the discrimination and segregation experienced by Muslim women, he added.
Some Muslims have accused him of wrongly “conflating” the two issues.
The government says 22% of Muslim women in England speak little or no English.
Launching a range of new measures, the prime minister said “more assertive” action was needed to tackle discrimination against Muslim women and their isolation in some UK communities.
As well as focusing on English language, he also announced a review of the role of Britain’s religious councils, including Sharia courts, in an effort to confront men who exert “damaging control over their wives, sisters and daughters”.
Segregation, he argued, was allowing “appalling practices” such as female genital mutilation and forced marriage to exist, and increasing vulnerability to recruitment by so-called Islamic State – also known as Daesch.
‘More susceptible’
Speaking to BBC Radio 4’s Today programme, Mr Cameron said the push on language was “about building a more integrated, cohesive, one nation country where there’s genuine opportunity for people”.
“I think in the past people have thought that the progressive thing to do was to allow people to come to our country and leave them to develop separately in their own ways. I think that is completely wrong.”
He said some “menfolk” in Muslim communities were fostering segregation by preventing women from learning English or leaving home alone, adding: “It’s holding people back, it’s not in tune with British values and it needs to go.”
Mr Cameron said there was “a connection with combating extremism” and improving English was important “if we’re going to try to help people become more resilient against the messages of Daesch”.
“I’m not saying there’s some sort of causal connection between not speaking English and becoming an extremist – of course not, that would be a ridiculous thing to say,” he continued.
“But if you’re not able to speak English, you’re not able to integrate, you may find, therefore, that you have challenges understanding what your identity is and you could be more susceptible to the extremist message that comes from Daesch.”
BBC political correspondent Ross Hawkins says the government’s counter-extremism strategy has previously been criticised by the Muslim Council of Britain as being based on fuzzy conceptions of British values.
Dal Babu, a former chief superintendent with the Metropolitan Police who now works with families whose children have gone to fight with IS, told Today the investment in language lessons was welcome.
But he added: “My concern is how we have conflated the issue of learning English with stopping radicalism and extremism… to conflate the two is unhelpful.”
Mr Babu also said he did not recognise the figure of 22% as the proportion of Muslim women without good English – instead quoting a figure of 6%, cited by racial equality think tank the Runnymade Trust.
Dr Sundas Ali, a lecturer at Oxford University who researches Muslims in Britain, said language might be a barrier for some women, but there were much bigger factors.
“I think there’s an overall cultural problem in a lot of the Muslim community which is of low expectations. I think Muslim women are not encouraged as much as non-Muslim women to excel in their education and their careers.”
She agreed there was no automatic link between not speaking English and being radicalised, but added: “Overall, I see what he [David Cameron] is trying to do and I do appreciate that, but I think there are other issues affecting Muslim women which he should have mentioned, such as hate crimes.”
The language lessons will be targeted at “specific communities” identified by a review into segregation that is being conducted by Louise Casey, head of the government’s “troubled families” unit.
They will take place in homes, schools and community facilities, with travel and childcare costs – described as “some of the greatest barriers to participation” – being covered. An existing scheme is said to have helped more than 30,000 adults.
The PM acknowledged cuts had been made to free language classes for immigrants during the last Parliament, but said the new £20m fund was “more targeted”.
He also said women who came to the UK on a spousal visa could be deported if they failed to learn English by the time that visa ran out.
“They can’t guarantee that they’ll be able to stay,” he said, insisting that people who wanted to settle in Britain permanently had a responsibility to learn the language.
