Newry and Armagh MLA Conor Murphy made the comment following the first roundtable discussion of the new year after the talks were paused for the festive period.
PICTURES: 9 images of protestors outside Stormont todayHe told media he sees "no need" to draw the talks out until the January 13 deadline.
The latest process, which was initiated in the wake of the general election, was paused over the festive period after a pre-Christmas deal failed to materialise.
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Secretary of State Julian Smith, Irish foreign affairs minister Simon Coveney and the local parties returned to Stormont House on Thursday morning to resume the effort.
The Democratic Unionist Party and Sinn Fein held separate meetings with Mr Smith, before a roundtable with the other Stormont parties and the Irish Government.
Further bilateral meetings are expected to continue throughout the day.
Mr Murphy said the first roundtable meeting had lasted 30-45 minutes.
"We think agreement can be reached in short order, we don't see any need to run this down to the wire to January 13 in some kind of dramatic way," he said.
"The issues that we are dealing with are all well rehearsed, what we need now is political will to get down to resolving very very quickly and that is going to be our focus in the next day or two."
He said agreement remained to be reached on a number of issues.
Mr Murphy outlined some of the issues where agreement remains to be reached.
"There are obvious ones around language provision, the petition of concern and its usage, but there are also issues this afternoon which will be talked out around programme for government, financial resources available to any new Executive," he said.
"This place can't function if we can't deliver for public services, we can't just sit here and be an instrument of Tory austerity. We have to have sufficient public resources to be able to deliver services which recognise the particular circumstances in this part of Ireland and the difficulties we face.
"There are a range of issues which will be discussed in the next couple of days. None of them, I don't think, need to be exhausted ad infinitum, we need to be bring this to an conclusion. There are pressures continuing to mount in relation to public health, health services and the treatment of staff in the health service. We need to get back working again so we can fix those as quickly as possible."
From Thursday morning a number of protesters stating their opposition to an Irish Language Act being included in any potential deal set up camp outside the talks venue holding aloft union flags.
Three years on from the collapse of the devolved government, the Stormont parties have until a January 13 deadline to strike a deal to revive the institutions.
On that date, legislation to give civil servants additional powers to run Northern Ireland's struggling public services expires and Mr Smith will assume a legal obligation to call a snap Assembly election.
The latest push to restore powersharing broke up the week before Christmas, with UK and Irish governments singling out the DUP as the party standing in the way of a deal.
The party rejected the claims, insisting it would not be "bounced" into a "quick fix" that falls apart when tested.
Devolution can only be restored once the DUP and Sinn Fein - the region's two largest parties - agree terms to re-enter a mandatory coalition executive in Belfast.
The other three main parties - the SDLP, Ulster Unionists and Alliance - are also involved in the talks process convened by the UK and Irish Governments.
While they could take positions in any new executive, their sign-off on a deal is not essential and a government could be formed in their absence, with those parties having the option of going into opposition.
Expectations of a breakthrough rose after the DUP and Sinn Fein both suffered bruising results in the general election.
With many interpreting the outcome as a public judgment on the parties' failure to do a deal, stalled efforts to restore the institutions appeared to gain fresh momentum in December.
However, proposals to reform a contentious cross-community voting mechanism in the Assembly have emerged as a key sticking point in efforts to finalise an agreement, with the DUP unhappy about what is being countenanced.
The DUP is also seeking changes to ensure the devolved institutions are more stable in future and cannot be readily pulled down.
Proposed legislative protections for Irish language speakers are another crucial element of the negotiations.
The Stormont parties are also seeking firm commitments from the UK Government on a financial package to accompany the return of devolution - money that would likely be targeted at the region's crisis-hit health service.
Mr Smith and Mr Coveney were in Belfast on New Year's Day for pre-talks discussions ahead of the resumption of formal exchanges with the political parties.
Mr Coveney urged the parties to show leadership and generosity.
He said the new year offered a chance for a new beginning and urged all sides not to disappoint the public again.
The leaders of the DUP and Sinn Fein used their respective new year messages to restate a desire to return to government.
DUP leader Arlene Foster said her party stood ready to restore devolution through a "fair and balanced deal".
"A Northern Ireland that is going to keeping moving forward must be one where everyone feels at home but must also be one where no one feels their culture is being marginalised," she said.
While Ms Foster warned that a focus on a potential border poll would lead to a "wasted decade", Sinn Fein president Mary Lou McDonald insisted a united Ireland was within reach.
But the republican leader added: "There is no contradiction in working for Irish unity and working for the restoration of the Executive and Assembly - they are all part of the Good Friday Agreement.
"The outstanding issues can be resolved. The time for acrimony and division is over. The time for slogans and soundbites is over. The test now for every party that has talked up getting back to work is to go back to the Executive table and deliver."
Stormont imploded three years ago this month when the late Sinn Fein deputy first minister Martin McGuinness resigned in protest at the DUP's handling of a botched green energy scheme.
That dispute soon widened to encompass traditional rifts over issues such the Irish language and the toxic legacy of the Troubles.
A logjam over proposals to reform the petition of concern voting mechanism was one of the main reasons a deal failed to materialise before Christmas.
It was designed to protect minority rights but politicians have accused each other of misusing it for their own ends.
Discussions around change are focused on making it more difficult for one party to use the petition to block controversial legislation.
The parties are also considering amending Assembly rules to make it harder to collapse the institutions.