The DUP's deputy leader Nigel Dodds has said the party "doesn't give blank cheques to anybody" when it comes to supporting prime minister Theresa May.
It comes just days before the cabinet is set to hold crunch talks on the government's approach to Brexit.
Mrs Foster also said the prime minister is "looking at a range of options" regarding the deadlock at Stormont.
EU backstop 'not acceptable'
Asked whether the DUP would support Mrs May regardless of the turmoil, Mr Dodds replied: "We don't give blank cheques to anybody."
Referring to the agreement signed last June, Mrs Foster added: "We are still very clear about what we signed up to."
Mickey Brady, the Sinn Féin MP for Newry and Armagh, accused the DUP of being "dishonest and hypocritical" over its support for Mrs May.
"The DUP are propping up a government that has brought us austerity, public service cuts and a chaotic Brexit," he said.
"It is dishonest and hypocritical for them to complain about cuts to services while propping up the government responsible for these cuts."
Mr Dodds said that the prime minister "didn't go into any details" of a reported third model for handling customs after the UK leaves the EU.
"We discussed the need to make sure that the EU have a comprehensive policy from the UK government, that the position of Northern Ireland should be very firmly confirmed, that there is no border down the Irish Sea.
"She was very firm on that point...there will be no breaking up of the UK economically, constitutionally or politically."
The DUP deputy leader accused Taoiseach (Irish prime minister) Leo Varadkar and EU governments of using the Northern Ireland border to try to "bully and intimidate" the UK government in Brexit negotiations.
'Crying out for decisions to be made'
"The EU backstop is not acceptable to us and not acceptable to the prime minister," he said.
"The prime minister has been clear that we are leaving the customs union and the single market."
Last week, the UK government said it planned to take further steps to ensure good governance in Northern Ireland, which has been without a devolved government since January 2017, including "legislative intervention".
DUP leader Arlene Foster said the prime minister is looking at "options" and added: "Everyone is crying out for decisions to be made in Northern Ireland on a range of matters."
In next week's budget bill around £400m is expected to be made available for health, education and infrastructure.
The confidence and supply agreement saw the DUP secure a financial package for Northern Ireland in exchange for support on certain issues.