DUP deputy leader Nigel Dodds, speaking shortly after the 200-117 vote of confidence in the Prime Minister, said his party's focus was on the draft agreement.
A spokesman urged her to bring it back before the Commons without delay, warning: "The parliamentary arithmetic remains unchanged".
Theresa May has appealed to European Union leaders to give her the assurances she needs to get the backing of MPs for her Brexit deal.
"I will contest that vote with everything I've got", she said.
"Over the last two years I hope I have shown that you can trust me to do what is right, not always what is easy, however hard that might be for me politically", she told leaders.
After the result of the Conservative MPs' vote, Ms Sturgeon said: "She may have clung on to the Conservative leadership, but her remaining authority has been fatally undermined".
Before the vote, May promised to step down from her role before the 2022 election.
May has been attacked from all political avenues by her management of Brexit.
What happens to the Brexit process now, as Prime Minister Theresa May fights a challenge to her leadership? She produced another bravado performance at prime minister's questions, where she bested the opposition Labour party leader, Jeremy Corbyn.
However, she made clear she was not expecting an "immediate breakthrough" during the course of the two-day gathering in the Belgian capital.
Former Ukip leader Nigel Farage tweeted that Mrs May "limps on to her next failure, the deal won't pass and the real crisis is close".More news: Comey blasts Trump, Republicans after meeting with House lawmakers
He said: "We can not go on like this".
On Monday 10 December she called for a parliamentary vote on the deal, which would see the United Kingdom maintain strong ties with the European Union.
In the early evening she addressed her electorate of Tory MPs at a meeting of the 1922 Committee, where she told members that she would not stand as leader at the next general election, a widely trailed concession which was believed to be a necessary to shore up support.
"I am in no doubt that the best result for all of us is to get this deal delivered in an orderly way and to get it done now".
"The issues that we came into politics to deal with, building a stronger economy, delivering first-class public services, building the homes that families need".
This morning, it was announced that at least 48 disgruntled Conservative Party MPs had written letters of protest in support of ousting the Prime Minister.
Meanwhile, Nadine Dorries, a Brexiteer Tory MP, said: "If MPs with small majorities vote to keep the Prime Minister tonight, they will be voting to secure her in place for the next 12 months, which means she will very likely lead us into the next General Election".
May has said she is seeking "legal and political assurances" over clauses in the text created to keep the border with Ireland open.
Theresa May's authority has been "fatally undermined" despite winning a confidence vote, Nicola Sturgeon has said. They could push for a "plan B", which would see Britain adopt a softer Brexit, such as staying in the EU's satellite trading bloc the European Economic Area - the so-called Norway option.
Mrs Foster, whose 10 MPs prop up the minority Conservative administration, said she told the PM that "we were not seeking assurances or promises, we wanted fundamental legal text changes".