Mr Varadkar says the EU referendum result is not good for Ireland or Britain
The minister for social protection says cross-border workers rights must be protected.
But Leo Varadkar says he is "saddened" by the result of Britain's EU referendum.
He told The Right Hook here on Newstalk: "I don't think it's good for Ireland or for Britain or for Europe."
As the Government publishes its contingency plan, Mr Varadkar has moved to reassure Irish workers and pensioners in Britain that "all their benefits, payments and obligations remain in place".
On the issue of bilateral agreements between the two nations, Mr Vradakar says: "We can have bilateral agreements with the United Kingdom...but what we can't do is have one that is contrary to European law.
"We will still be part of the European Union and therefore bound by the European laws...which we sign up to."
He also says any such bilateral agreements will have to be agreed by the European Union as well.
"We don't know exactly how long this will take...but certainly a two-year timeframe is what everyone's talking about, and that's what provided for in the treaties."
Minister Varadkar says there are three key areas for the Irish Government on any negotiations.
"A key thing for us will be trying to keep Britain in the single market - which is important for trade - trying to retain the common travel area so that we don't have border controls between the North and the Republic...and also to make sure that those protections that are afforded to pensioners and workers moving across borders are protected," he added.