"We will work with the crossbench on the basis of a new package of measures flagged at the end of last year."
Mr Dutton has signalled he is willing to cede some ground in negotiations with the crossbench.
However, he would prefer to secure bipartisan support rather than dealing with an unpredictable assortment of independents, urging the Labor Party to shift its position.
"If they don't, I'm confident that (Citizenship Minister) Alan Tudge can deal with the independent senators and negotiate an outcome to the package."
The government initially wanted to lift English requirements from "basic" to "competent", which would require aspiring citizens to understand fairly complex language and have an effective grasp of English.
It has since agreed to accept a "modest" level, meaning would-be Australians must be able to handle basic communication and have a partial command of the language, while making many mistakes.
The government also wanted to impose its crackdown retrospectively, capturing everyone who applied for citizenship since its policy was announced on April 20, 2016.
It is now willing to hold fire on the changes until July 1 this year.
The Nick Xenophon Team, whose bloc of votes was critical last year, were not immediately won over by the watered-down changes, but their power has since been diminished by the fall-out from the dual citizenship saga.