All 27 members states must ratify the treaty before it becomes law
Conservative leader David Cameron has told Gordon Brown to show "backbone" and declare the EU treaty "dead".
He was speaking as the House of Lords prepared for a vote which could ratify the treaty, despite voters in the Irish Republic rejecting it in a referendum.
At prime minister's questions Mr Cameron said: "This is not a treaty Britain wanted or needed."
Mr Brown said he respected the Irish vote - but ratifying it showed respect for the MPs who had voted for it.
He added: "Just as we have respect for the Irish, we should have respect for the other countries that are processing the treaty and ratifying the treaty as well.
"And perhaps we should also have respect for this House, which has also voted for ratification of the treaty."
But Mr Cameron said: "Either this treaty is dead or it isn't. I simply don't understand why you don't have the courage to say that it is dead.
"Because you won't take a lead and declare the treaty dead, everyone suspects you and others in Europe are going to make the Irish vote again.
"Will you guarantee that you would never support such an arrogant and high-handed move.
"It would be ridiculous to ask the Irish to vote twice, when we haven't even been allowed to vote once."
The House of Lords has begun debating whether to ratify the EU reform treaty - its final Parliamentary hurdle.
During a question about the treaty, a woman was removed from the public gallery after shouting: "Give us a referendum."
It could be given Royal Assent on Thursday and the government would then deposit documents known as "instruments of ratification" in Rome.
But it will not come into force until all 27 countries have also deposited their instruments of ratification.
If one or more countries does not ratify the treaty, a future British government could withdraw from it.
Conservative peer Lord Howell has tabled an amendment to delay the third reading of the bill to until 20 October in the light of the Irish vote.
EU foreign ministers have said member countries which have not yet ratified the treaty should still press ahead.
Lord Howell told BBC News: "The situation has changed totally.
"Our duty as an amending chamber is to really give the elected chamber, the Commons, a chance to look at it again and they certainly should do so.
"We do that by postponing it and then amendments can be moved later.
"The thing needs thinking about and it seems bit silly to close it all down now and ratify a treaty which is technically dead."
Foreign Secretary David Miliband has said the Irish result should be respected but there should also be a "British view" on the treaty.
Foreign ministers will meet for a two-day summit in Brussels on Thursday which is expected to chart the way ahead.
The Lisbon treaty aims to streamline the decision making of the European Commission but critics say it will transfer more power to unelected officials in Brussels.
It includes removal of the national veto in more policy areas, a new president of the European Council and a strengthened foreign affairs post.