The taoiseach (Irish prime minister) says the EU is "happy to offer assurances" to the UK about the Brexit deal, but that the backstop is not up for negotiation.
He made the comments after a meeting with Prime Minister Theresa May.
Mrs May is attempting to get political and legal reassurances about the Irish border backstop.
Leo Varadkar spoke to the press after what he described as a "long meeting" with Mrs May on Thursday morning.
During the meeting, Mr Varadkar said Mrs May outlined "some of the difficulties she's facing", and that he "had an opportunity to give her Ireland's perspective".
"The deal we have is the only deal on the table," said Mr Varadkar.
"We're happy to offer explanations, assurances, clarifications to help MPs understand the agreement and hopefully support it, but the backstop is not on the table.
"We'll have to work out exactly what those assurances are and what formation they will take."
Asked if the assurances should be legally binding, Mr Varadkar replied: "I don't think we could agree to anything that would change the content of the withdrawal agreement."
Meanwhile, Mrs May said she will be showing EU leaders the "legal assurances" she believes MPs want before they will back her deal.
She said she was not expecting a breakthrough on the backstop at the two-day summit.
"My focus now is on ensuring that I can get those assurances that we need to get this deal over the line, because I genuinely believe it's in the best interests of both sides - the UK and the EU - to get the deal over the line, to agree a deal.
"But I recognise the strength of concern in the House of Commons and that's what I will be pushing to colleagues today.
"I don't expect an immediate breakthrough, but what I do hope is that we can start work as quickly as possible on the assurances that are necessary."
EU leaders are likely to reaffirm to Mrs May that the backstop is only an insurance policy which they do not want to use.
But other leaders arriving on Thursday emphasised that whatever assurances are given they cannot contradict the deal that Mrs May agreed last month.
'Cannot be contradicted'
Mrs May was due to meet Leo Varadkar on Wednesday, but their talks were cancelled due to the vote of confidence in her leadership.
She has met other EU leaders in recent days, but they have given no indication they are prepared to make major changes to the Brexit deal.
On Wednesday night Mr Varadkar spoke to European Commission President Jean Claude Juncker.
They agreed the withdrawal agreement is "the best outcome available" and "cannot be reopened or contradicted".
The Irish government has been consistent that whatever happens in the Brexit process there will be no hardening of the Irish border.
Asked earlier this year, Mr Varadkar said: "That will just never happen - ever."
What is the latest on the backstop?
The prime minister says she will be showing EU leaders the "legal assurances" on the backstop she believes MPs want before they will back her EU withdrawal deal.
Critics say the backstop - the plan to avoid a return to a hard Northern Ireland border - will keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals.
The EU says it will not renegotiate the backstop, but may agree to greater assurances on its temporary nature.
What is the latest EU position?
The BBC understands that any reassurances offered to Mrs May could centre on an attempt to "detoxify" the idea of the backstop for Westminster.
Its temporary nature could be emphasised, along with the EU's readiness to keep searching for a better alternative even if the backstop were ever to be triggered - both stronger reassurances to the policy's critics than offered in the past.
For example, a draft of the European Council conclusions on Brexit says the EU would use its "best endeavours to negotiate and conclude expeditiously a subsequent agreement that would replace the backstop so that it would only be in place for a short period and only as long as strictly necessary".
In other words, the EU would continue trying to negotiate a trade deal with the UK even if the Irish backstop had been triggered at the end of the transition period. The Brexit withdrawal agreement only talks about "best endeavours" being used to reach an agreement during the transition period.
What is the DUP's view?
The DUP has branded the backstop "unacceptable" and has repeatedly said it would not accept any additional Northern Ireland-only customs checks, because it is concerned that any differences between NI and Great Britain could threaten the union.
DUP leader Arlene Foster has said that "tinkering around the edges" of the agreement would not be enough to win the support of her party, which wants "fundamental legal text changes".