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Arlene Foster said that there was still time to negotiate a better deal and that the DUP would vote against if the backstop was not removed.
The leader, Arlene Foster, is said to be "disappointed" by Theresa May and the government's decision to advance the Brexit deal.
The UK withdrawal agreement from the European Union has been approved by EU leaders.
But Ms Foster reiterated that the DUP, which supports the government, will vote against it in Parliament.
The plan has aroused political opposition because of the security that aims to avoid a difficult Irish border.
Ms Foster said the agreement "went against everything" the DUP had been promised.
The backstop agreement would only see Northern Ireland staying aligned with some EU rules, if it came into effect.
The DUP fears that the safety net may threaten the integrity of the union and place a trade border along the sea of Ireland.
At the annual DUP conference on Saturday, Westminster party leader Nigel Dodds called on the prime minister to "reverse the situation."
Arlene Foster, who appeared on the Andrew Marr show Sunday, said: "We are disappointed with the way things went.
"Theresa May is a trade unionist, but this deal goes against everything she's said about all this."
The DUP has repeatedly stated that it will vote against the agreement, as it stands, when it will be ratified by Parliament within a few weeks.
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Pacemaker
Senior Conservative MP Boris Johnson delivers Keynote Address at the DUP Annual Conference
Ms. Foster said that there was still time to negotiate a "better deal".
"Conversations across the government"
"We should use the time now to look for a third way, I recognize that we are dealing with fatigue, there comes a time when everyone is tired and just wants to continue, but we should not accept the result for good", was -she adds.
Several newspapers reported that the DUP was involved in discussions with several government ministers over a secret "Brexit B plan", though Ms. May's agreement had not passed in the Commons .
Ms. Foster did not explicitly deny the report, but said her party was having "discussions across the government" about the deal.
She also stated that she currently did not see any circumstance in which Ms. May's agreement would have enough support to be passed by Parliament.
The DUP holds the balance of power in Westminster, the government relying on the votes of its 10 MPs to get a majority of work in parliament.
He signed a trust and supply pact with the Conservatives in June 2017 and negotiated additional spending of £ 1 billion for Northern Ireland – but the disagreement between the parties on the Brexit's plan exerted considerable pressure on the agreement.
Ms. Foster has already stated that if the government agreement is passed in the House of Commons, the DUP should review the confidence and supply pact.
"We will look at it then: the situation is fluid, things are changing, we will have to see where we are," she added.
The government insisted that it would not renegotiate the current plan and urged MPs to support it or risk a no-deal scenario.
