Money being offered by the secretary of state to resolve Stormont's budget deadlock does not go far enough, Sinn Féin and the DUP have said.

The parties were speaking after the executive met Sir Chris Bryant, who arrived on Monday for talks about the issue.

BBC News NI understands that the initial offer to the executive was £350m a year over the next three years. But the executive is believed to have said it needs £450m annually to meet its pressures, leaving a gap of £100m each year.

The executive has said it cannot agree a budget for this financial year without additional support from the Westminster government.

Following the passing of a deadline in August, Stormont officials were given legal powers to spend up to 95% of last year's funding in the absence of ministers agreeing the budget.

Last week, Prime Minister Andy Burnham pledged to get the Stormont government functioning properly with a budget, but it is unclear how much money London could provide.

Sir Chris held talks with the executive on that issue, as well as seeking the parties' views on potential reform of the institutions.

He held talks with the executive before meeting party leaders and holding one-to-one bilaterals with the five largest parties.

Speaking after meeting the secretary of state, First Minister Michelle O'Neill said the executive was now in a "negotiation" with the government.

"We get to this juncture time after time, crisis point after crisis point - they need to fix the baseline.

"If they throw a few pounds on the table and walk away we'll end up back in this scenario."

DUP leader Gavin Robinson said the assembly was returning with a bit of "vim" after the summer break, and that the budget needed urgent focus.

"My understanding is at this stage, resource has been offered but it falls well short of even some of the pressures in one department, let alone across the Northern Ireland Executive.

"Anybody who says we just need to get on and agree this can explain the cuts that will come as a consequence."

Asked how long the talks could take, he said he did not think there would be a resolution this week.

It is not clear yet how much money exactly could be on the table from Westminster.

The SDLP - Stormont's official opposition - was not part of the executive discussions on the budget, but a delegation of its politicians is meeting the secretary of state to discuss another issue on Monday - potential reform of the institutions.

Alliance and the SDLP have long called for the power-sharing institutions to be reformed to prevent them from collapsing again.

Leader Claire Hanna said there did not need to be a "long period of diagnosis".

"We don't need months and months of negotiation in a stately home, everybody knows what needs to be done.

"If they're not done we're going to be right back here and if we fail to put these mechanisms in place ahead of the next election we're facing into more lost years."

In June, Sinn Féin - the largest party at Stormont - published its own proposals urging similar measures to be introduced.

It called for the removal of what it called a "veto" on executive formation - namely the nominations of parties to the roles of first and deputy first minister.

If the largest party within nationalism or unionism in Northern Ireland refuses to nominate for the role an executive cannot be formed.

Sinn Féin is arguing that in future, if either of those parties chooses not to nominate, the opportunity to take up the role should pass to other parties.

It said this would ensure the institutions can continue to function while maintaining the principle of power sharing.

The use of the veto has been used by both Sinn Féin and the DUP in the past and has been criticised by smaller parties at Stormont.

Any changes to the current structures would require the UK government to legislate for them.

It is not clear how quickly the secretary of state wants to progress discussions on this area, with the next assembly election due in May 2027.

TUV leader Jim Allister said the system of executive devolution was fundamentally flawed, but that reform should not be the priority when basic governance is a struggle.

"We simple think patch it here, patch it there but never face the reality that it's a system built on sand that is incapable of working."

Speaking before talks, UUP MLA Steve Aiken said he was "quite hopeful that the secretary of state is going to say there is more money on the table today", given the Chancellor John Healey is expected to say the UK economy is "turning the corner" in his first major speech since taking the role.

Also speaking on Good Morning Ulster, he said any funding "has to be linked to some sort of reform".

"If we are getting extra money, and I think we are due extra money and we should be getting extra money, it should actually be tied to make sure that Northern Ireland is run much more effectively."

Alliance deputy leader Eoin Tennyson said that the issues around finances "cannot be divorced" from political stability and the need for reform around the institutions.

"I believe there is now a real momentum and if we are serious about breaking this cycle of crisis and collapse... We need to grasp the nettle in reforming the institutions," he told the programme.

Tennyson said he believes that Northern Ireland is not getting a "fair deal" compared to Scotland and Wales adding this was "not a sustainable position".