Sinn Fein president Gerry Adams called for David Cameron to fulfil his obligations under the Good Friday Agreement, warning that the peace process was in a "state of stagnation".
The Prime Minister met a Sinn Fein delegation for the first time, with Mr Adams joined by Northern Ireland's Deputy First Minister Martin McGuinness for the "very frank" talks.
Mr Adams said that Mr Cameron was aware there were "difficulties" in the process and would meet Sinn Fein again in the autumn.
Speaking to reporters outside the Palace of Westminster, Mr Adams said: "This is the first meeting that we have done as a Sinn Fein delegation with the British Prime Minister.
"We made the point to him that he is not fulfilling his obligations in terms of the Good Friday Agreement, that the process is in a state of stagnation at this time."
Mr Adams said he had made the point to the governments in both Dublin and Westminster that they needed to demonstrate "leadership and a fulfilment of their obligations".
The meeting, and fresh talks at Stormont, come six months after marathon negotiations chaired by former US diplomat Richard Haass ended without agreement.
While draft proposals outlined by Dr Haass remain on the table, with the party leaders having met periodically to discuss the outstanding issues since January, efforts to strike a deal in his absence have made little progress.
Mr Adams, who also met Labour leader Ed Miliband, warned that the height of the marching season in July could be a "potential disaster".
He said he told Mr Cameron the proposals put forward by Dr Haass and Meghan O'Sullivan "should have been welcomed and positively supported by his Government".
He added: "In all of this we think it was a useful meeting, it was a very frank meeting, and we made our views very, very clear.
"Too many people have invested too much in this process - and I'm not talking about politicians, I'm talking about ordinary people back home, people who want to live in peace, who want to look forward to July as a summer month as opposed to a month of possible disaster.
"People want to live with their neighbours in tolerance, have their own strong views but are prepared to respect others' views.
"In our opinion that's the vast majority of the folks back home."
He criticised the " negative interventions" by Northern Ireland Secretary Theresa Villiers and said "w hat we need is this Government to be a champion of the Good Friday Agreement".
But he said Mr Cameron was " indicating an awareness that there are difficulties in the process" and added: "In that case what we need is action, what we need is him to fulfil his obligations under the terms of these agreements and for the Taoiseach to do the same."
Before the bilateral meeting with Sinn Fein, Mr McGuinness and First Minister Peter Robinson held talks with Mr Cameron and Ms Villiers in the Prime Minister's office in Parliament.
Mr Cameron has insisted Northern Ireland's economic recovery is well on course, a year on from the implementation of a Government-backed stimulus package aimed at cementing political gains made in the post-conflict era.
"It is great news that the long-term economic plan is working for Northern Ireland," he said.
A mainstay of the package was giving the Northern Ireland Executive the ability to borrow an additional £100 million from the Treasury.
But discussions about he economy were overshadowed by a row about Sinn Fein blocking welfare reforms in Northern Ireland, which has led to financial penalties from the UK Government.
Mr Robinson said he was "outraged" about the situation and claimed that the position adopted by Sinn Fein and Mr McGuinness would damage vital services including in healthcare.
He said Sinn Fein " either doesn't get it or doesn't want to get it".
"But the reality is that we are being penalised," he said.
"You can't wipe that away, the budget is being reduced because of the failure of Sinn Fein and the SDLP to take decisions.
"Those decisions would allow us to proceed with a larger budget than we now will have and, as a result, there will be penalties that will cause a reduction to front line services, particularly in health."
He added: "I think that it's impossible for any intelligent person not to know what the consequences of their action is.
"I'm outraged that people would allow the Northern Ireland community to suffer as a result of a failure to have the courage to take a decision that they know is necessary."
But Mr Adams said: "Sinn Fein's position on terms of the rights of citizens, particularly those citizens who are vulnerable, who need the state, society, to wrap itself around them, we make no apologies for that whatsoever.
"And there are as many people in that category who are unionist as there are people from any other background.
"We also believe that the cuts, which are ideologically driven by this Tory Government, are too big a cut for a small, retarded economy like the one in the north."
Mr McGuinness added: "We are not in conflict with Peter Robinson and the DUP on the issue of welfare.
"We are in conflict with the British Government and we said that to David Cameron during the course of the meeting."
Ms Villiers said the Government was sticking to its position on welfare reform and "there is no scope for negotiation, there is no more money on the table".
She said the UK Government was not imposing a penalty on Northern Ireland, "it's just the difference between the more costly system of welfare that the Northern Ireland Executive wants to run and the reformed system which has been introduced in the rest of the UK".
She added: "They can't expect taxpayers across the rest of the UK to fund that more expensive system.
"If they want a more expensive system that means they have less money to spend on other priorities.
"That's a point the Prime Minister made very clearly in his discussions today."