The DUP leader urged rivals to come together to strike a deal to resurrect the devolved executive ahead of another round of talks in Belfast.
The DUP and Sinn Fein go into the negotiations on the back of disappointing election results - with many interpreting the General Election as the public passing judgment on the parties' failure to restore the Assembly.
Northern Ireland Secretary Julian Smith will hold a round of bilateral meetings with the DUP, Sinn Fein, UUP, SDLP and Alliance Party at Stormont House on Monday morning, with a roundtable session with all the party leaders due later in the week.
Irish Foreign Minister Simon Coveney will also be at Stormont on Monday afternoon for talks.
It is understood that Mr Smith has been working on proposals to break the impasse which he will outline to the parties later.
A spiralling crisis in the region's health service has heaped further pressure on the politicians to get back to work in a devolved legislature.
Healthcare workers will go on strike on Wednesday to protest at pay restraints and staffing shortages.
Ahead of the meetings on Monday, Ms Foster said: "It is a shame on all politicians in Northern Ireland that we have not been able to have the institutions up and running again, but we have to now."
She told BBC Radio Ulster: "I fundamentally believe that if there's a will there is a way, and the issues have been talked about now for three years, so there is nothing new on the table - therefore there is every chance we can come to an agreement but there has to be a willingness across the piece.
"For my part there is certainly a willingness from the Democratic Unionist Party."
Sinn Fein's Stormont leader, Michelle O'Neill, said the institutions have to be restored on a "credible and sustainable basis".
"A credible restored Executive must deliver on issues such as public sector pay, safe staffing levels in the health service, economic policies that deliver prosperity and invest in rural communities, and an appropriate welfare mitigation package," she said on Sunday night.
"We will work towards securing agreement on outstanding issues, including an Irish Language Act, reform of the Petition of Concern (contentious Assembly voting mechanism), the legacy of the past and integrity in government.
"I believe they can be resolved if there is the political will to do so. We need a new kind of politics, a new Assembly and a new Executive.
"We need to deliver good government and properly resourced public services to all. We need an Executive which is transparent, accountable and inclusive."
Powersharing imploded almost three years ago amid a row about a botched green energy scheme.
That rift soon widened and refocused on long-standing disputes over issues such as the Irish language and same-sex marriage.
With same-sex marriage having been legislated for at Westminster earlier this year, the wrangle over the Irish language remains the key stumbling block.
Sinn Fein has made an Irish Language Act a prerequisite of any deal to restore devolution.
The DUP has expressed a willingness to legislate to protect the language, but only as part of broader culture laws which also include the Ulster Scots tradition.
Ahead of the renewed political talks involving the parties, senior health leaders, representing doctors and nurses in Northern Ireland, issued a statement outlining their serious concerns about the situation in the health and social care system.
The British Medical Association, Royal College of Emergency Medicine NI, Royal College of Surgeons of England, Royal College of General Practitioners (NI), Royal College of Nursing, Royal College of Psychiatrists NI, the Royal College of Radiologists UK and the Northern Irish Board of the Royal College of Anaesthetists - which collectively represent thousands of medical and nursing professionals in Northern Ireland - said they were taking the "unusual" step of issuing a joint statement due to the severity of the situation.
The groups called on politicians to get the devolved institutions up and running again with immediate effect.