Foster said the DUP wants to "support the national interest" and "bring stability to the nation".
Theresa May will meet the DUP leader Arlene Foster later, whose support the PM will need in order to get her Queen's Speech passed through Parliament.
It comes after the Prime Minister apologised to her MPs for the election result, telling them: "I got us into this mess and I will get us out of it."
The first move in Mrs May's new reality of compromise politics is to listen to what the DUP hope to gain by offering the Conservatives their support.
It is thought the Prime Minister is preparing to ditch unpopular policies such as her social care reforms and plans to means test the winter fuel allowance.
Arlene Foster said her party wants to "support the national interest" and "bring stability to the nation".
"We enter these talks in a positive fashion, we are first and foremost unionists and therefore we want to secure the union," she said.
"But we do want to do so in the national interest to give stability to the Government and that's why we will be entering these negotiations."
Mrs May will also hold her second Cabinet meeting in two days. One senior Conservative source told UK media that "a head of steam" was building for a "softer Brexit", with "significant people" pushing, but said the PM is "still unconvinced".
Mrs May will later travel to Paris to meet French President Emmanuel Macron to discuss online radicalisation.
He and other EU leaders are no doubt keen to know where her problems have left the Brexit negotiations.
Eurosceptic Conservative MP John Redwood said: "We're going to make a great offer to Europe in terms of their access to us and continued presence of their citizens here in Britain - they are very welcome.
"So we are very, very positive, and I hope that Her Majesty's Loyal Opposition on this issue - when our Prime Minister is in Brussels arguing for the whole country - that they understand they said they wanted the same things and that's what she's trying to deliver."
Mrs May appears to have bought some time with her MPs in her meeting with them on Monday night - most emerged impressed with what she had to say.