"When it comes to preserving the integrity of the United Kingdom and clearly delivering for the people of Northern Ireland when it comes to the Good Friday Agreement, we've said from day one. that we would always stand by our word and not compromise when it comes to unfettered access in goods and services but also standing by the Good Friday Agreement", she said on BBC Breakfast.
Speaking to reporters on Monday morning, Mr Cameron said: "Passing an act of parliament and then going on to break an global treaty obligation is the very, very last thing you should contemplate. That is the fundamental objective of this bill", he told the MPs.
Ministers say this is a failsafe mechanism in case the European Union interprets the agreement, in particular the Northern Ireland Protocol created to avoid a hard border on the island of Ireland, in an "extreme and unreasonable" way.
Opposition to the Bill has been building among Conservatives since Brandon Lewis told MPs that the government planned to break the law.
Ahead of last night's Westminster session the prime minister was facing threats of a rebellion from within his own party as former Attorney General Geoffrey Cox said he would be voting against the legislation, which he claimed would cause "unconscionable" damage to the UK's reputation.
"I believe very strongly we should obey worldwide law. I believe the United Kingdom's word is its bond and I think this is damaging our global reputation for honesty and straight-dealing", Sir Roger said.
Sir Roger acknowledged he was in a "tiny minority" among Tory MPs but predicted others could rebel when the Commons comes to consider amendments to the Bill next week.
For Labour, shadow business secretary Ed Miliband - standing in for Sir Keir Starmer who is in coronavirus self-isolation - said Mr Johnson had only himself to blame for signing up to the Withdrawal Agreement.
In Brussels, EU officials rejected the UK PM's claims that the move was needed because the bloc had refused to take a "revolver off the table" in ongoing trade talks.
"I took a view that you fight this tooth and nail at every step". Others have quite clearly decided they want to hold their fire. "There is much to play for yet", he told BBC2's Newsnight.
This matters because Mr Johnson has threatened to walk away from the negotiations if a trade deal is not agreed before 15 October.
The big challenge for the negotiating teams is to resolve issues that "make this legislation irrelevant" in a bid to secure a deal that is acceptable to all parties, Mr Coveney said speaking on his way into a Cabinet meeting.
"We're committed to making a success of those negotiations".
The Democratic Unionist party, which opposed the Withdrawal Agreement because of the inclusion of the Northern Ireland protocol, also backed the government.
"Either he was not straight with the country in the first place or he did not understand it", said Miliband.
"Because a competent government would never have entered into a binding agreement with provisions it could not live with".
The European Parliament trade committee negotiator for EU-UK relations has said the European Union has made compromises and shown openness in its approach to trade negotiations with Britain, but would not proceed unless the UK's Internal Markets Bill is amended or withdrawn.
"We welcome the fact that this vital Bill has passed its second reading", a spokesman for the Government said. Both sides accepted the compromise to protect the open border, which helps underpin the peace process in Northern Ireland.