Taoiseach Leo Varadkar has said it is too early to say whether Britain has made sufficient progress in Brexit talks to allow them to continue on to the next phase.
Mr Varadkar was speaking to reporters in London following talks with British Prime Minister Theresa May at Downing Street.
The meeting took place as Brexit negotiations resume in Brussels, with Mr Varadkar the first EU leader to visit Mrs May since her speech on Brexit in Florence last Friday.
The Taoiseach said the decision on moving the talks on to the next round will be made by the 27 EU leaders when they meet in October.
He also said the Government wanted to make sure that the close relationship built up between the two countries in recent years is maintained after Brexit, as well as the common travel area.
Mr Varadkar added that he hoped to keep free trade between the two countries "because we share the view that free trade makes everyone better off".
The Taoiseach also said the two leaders were in a "shared space" on trying to get the Northern Ireland Executive up and running again.
After the meeting, he said that he does not see any advantage to holding another election in Northern Ireland in an effort to end the ongoing stalemate.
A row between Sinn Féin and the DUP over an eco-boiler scandal collapsed the power-sharing executive last January and there has been no executive in place since then.
A series of talks between the main parties aimed at restoring the devolved institutions at Stormont have so far been unsuccessful.
Northern Ireland Secretary of State James Brokenshire has previously indicated that if a resolution is not reached by mid-October, direct rule from London may be introduced.
Last Friday, Mrs May proposed a two-year transition period for the UK after its leaves the EU, suggesting that Britain would continue to "honour its commitments" under the bloc's current budget.
She also said that everything would be done to avoid friction at the borders.
Mrs May said there are "unique issues to consider when it comes to Northern Ireland".
She said the British and Irish governments, and the EU as a whole, have made it clear that progress made in Northern Ireland in recent years would be protected.
Minister for Foreign Affairs Simon Coveney said the UK "needs to bring a plan" to the table for Brexit.
Speaking on RTÉ's Morning Ireland, he said Mrs May did provide some welcome detail in her speech in Florence.
Mr Coveney said the Government does not want Brexit but that if Britain is determined to move ahead, then the Government wanted as close to the status quo as possible.
This would include, he said, Britain staying in the Customs Union and an extended single market.
When asked about the power-sharing talks at Stormont, Mr Coveney said the relationship between the DUP and Sinn Féin has improved, with trust being built between the leadership of both parties.
He said there was a lot of "quiet work" going on in Belfast and hoped that significant progress would be seen this week.
Hosting Rugby World Cup makes good economic sense - Taoiseach
Earlier, Mr Varadkar was on hand to assist Ireland's bid to host the 2023 Rugby World Cup.
The other two contenders, France and South Africa, also made formal presentations to the World Rugby Council at a Kensington hotel.
The final decision on the host country will be announced in mid-November.
"The government is underwriting the tournament in the confidence and reasonable expectation that there will be a net return to the Irish economy because of the number of visitors and economic impact in terms of VAT and excise," Mr Varadkar said.
"It makes it a very good business case, not just for the IRFU and World Rugby, but also the Irish economy and the Irish tax payer," he added.
Minister for Transport, Tourism and Sport Shane Ross has said he thinks Ireland's chances of hosting the Rugby World Cup in 2023 are "very good."
Speaking on RTÉ's Today with Sean O'Rourke, Minister Ross said the bid is really fantastic with a sound financial plan.
He said it is a national effort and the Taoiseach's presence at the presentation highlights the fact that the country and the Government are behind the bid.
Mr Ross said that there may be higher financial bids but he believed the World Rugby Council was looking for a new bidder and Ireland offered new openings to the council.
"The fact that it's a North-South bid, that rugby unites Ireland is something extremely important and is a huge selling point. We're offering a secure, modernised, financial bid but we're offering something new," he added.
Mrs May has also backed Ireland's bid as Mr Varadkar revealed that she has written to the Rugby World Cup organisation, affirming the UK's support for the tournament to be hosted here.