Stressing EU nationals shouldn't worry about being deported unless they have "committed a crime", the Brexit Secretary also insisted British tourists will still get free healthcare when they go on holiday.
MORE: Who is going to invest in the United Kingdom post-Brexit? Let me be absolutely plain about this, number one, I happen to think we have got a very good Prime Minister.
Davis also said Britain would likely need transitional trade arrangements with the European Union for up to two years after Brexit.
And, again, Davis sounded very cautious about the prospects of getting the kind of agreement Prime Minister Theresa May has pledged.
But he warned Tory MPs not to launch a bid to push out the Prime Minister in fear of destabilising the Brexit process. "I know she is coming under a lot of pressure at the moment, but I have seen her in action".
Asked if he agreed with the Chancellor that no deal would be very, very bad, Mr Davis said: "It would be better than a punishment deal".
Mr Davis has himself been tipped as a possible successor to Mrs May, alongside Foreign Secretary Boris Johnson and International Development Secretary Priti Patel.
Cabinet minister Liam Fox told his fellow Tories to stop "navelgazing" and called for MPs to support Mrs May rather than plotting against her.
He said: 'If the sillier people in the Conservative Party now decide that the best thing to do is start arguing about the leadership we will just make a very hard, very serious situation rather absurd.
He said: 'There is no essay crisis about this government.
Senior party figures are reportedly "lining up" Mr Hammond to replace Mrs May after the Tories lost their parliamentary majority in the general election earlier this month.
The plan to move the Chancellor into the top job will worry Brexiteers because Mr Hammond was a Remainer and is in favour of a so-called soft Brexit.
He added: "We can not have a circumstance where the other side says that they are going to punish you".
'What we want is to be able to have fair migration that avoids people's jobs being undercut'.
The Brexit Secretary said speculation among Conservative MPs about a possible leadership contest in the wake of the party's embarrassing loss of its Westminster majority at the general election was "self-indulgent nonsense".
"He and I have discussed this weekly since before Christmas", he said.