Mr Spring, who last night met Tony Blair, the Labour leader, for private talks, also urged Mr Major to reject the pressure by David Trimble, the Ulster Unionist leader, to proceed with the peace talks without Sinn Fein.
"The choice for Mr Major is to solve the Northern Ireland crisis. As opposed to depending on Mr Trimble's support, I think that Mr Major is big enough to go for the solutions to Northern Ireland's problems. I believe that," said Mr Spring.
His remarks touched on raw Tory nerves and are certain to anger some Tory MPs by appearing to engage in domestic party politics on his flying visit to London.
There is a growing fear among senior Tory politicians who are close to the Unionists that, rather than wait until next May, Mr Trimble will withdraw his support for the Government and trigger a general election in February to underline his party's importance.
The Unionists could become pivotal in the New Year, if the Tories lose their majority after the Wirral South by-election, following the death of Tory MP Barry Porter.
Speculation about bringing down the Government is rejected by Mr Trimble, but at a press conference at the Irish Embassy in London, Mr Spring was less dismissive.
There was no suggestion, he said, that the changes in the Clinton administration after the re-election of the President would lead to the recall of Senator George Mitchell, who has acted as chairman for the talks.
Mr Spring made it clear he wants progress in the talks, but Sinn Fein must be part of any final settlement. He said: "Sinn Fein don't have a veto. They are not going to stop the talks. I have no difficulty in seeking a momentum in the talks which has not been there.
"Notwithstanding that, we have an obligation to those who support constitutional parties to see if we can bring about an agreement between Nationalism and Unionism... The ideal is to stop the violence."
Mr Spring, who is in the centre of European moves to broker peace talks in the Middle East, said he had no indications - in spite of speculation of a secret IRA convention at the weekend - that there would be a ceasefire called before the general election.
"If we are going to have the ultimate accommodation it is going to require all parties sitting around the table," he said.
"It would be in everybody's interests to have the talks as quickly as possible and to have all parties at those talks," Mr Spring added.
"We want an unequivocal restoration of the ceasefire. We have said we want early entry of Sinn Fein to the talks. That is not to underestimate the difficulties caused by the Lisburn bomb, and the other bombs at Manchester and Canary Wharf.
"We have to overcome those difficulties. We will be looking closely at the nature of the ceasefire to know it is unequivocal and there can be no threat of going back to violence."Reuse content