The pair gave a joint press conference in Dublin as Brexit talks remain stuck over the Irish border question.
European leaders meet in Brussels next week but a deal is not expected to be struck on the divorce's implications for the 300-mile border with its multiple crossing points until at least another European Council summit in the autumn.
In December 2017 she achieved a provisional agreement covering Britain's £39 billion "divorce bill", future citizens' rights and the border between North Ireland and the Republic.
The EU wants the backstop to involve Northern Ireland staying in the single market and customs union indefinitely after Brexit.
Britain's plan for a temporary customs "backstop" is "not acceptable" and any fall-back option can not be time-limited, the European Parliament's chief Brexit co-ordinator has told MPs.
The missive follows a tumultuous week in parliament that saw prime minister Theresa May almost get through her Brexit bill after fears of a back bench backlash.
The Government says it will and Labour is also committed to taking Britain out of the European Union, despite significant unrest on the back benches.
"A withdrawal agreement without a backstop is of no use to us whatsoever", he added.More news: Iran vs. Spain live stream
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But the shape of that fall-back remains a sticking point, with the European Union rejecting a United Kingdom contention that it should only be temporary, even if a broader agreement fails to materialise. The EU says no substantial progress has been made in negotiations going into next week's summit.
"Your proven commitment to the European ideal will always find a home here, and our friendship will be steadfast as we work together towards a better Europe".
He added that drama in Westminster this week over the "meaningful vote" amendment wasn't helping efforts to solve the Irish border conundrum, saying: "British politics isn't my concern".
Mrs May faces an European Union summit on 28 June, at which both sides were hoping to demonstrate progress in the Brexit negotiations.
Varadkar called for intensified talks if both sides are to reach a deal by their target of October, to leave time for it to be ratified by the British and European parliaments by March 2019, when Britain is due to formally leave the bloc.
The Irish government was supported by Juncker, who said:"Ireland is not alone".
"I am strongly against any temptation to isolate Ireland and not to conclude the deal on Ireland".
The pair held a short meeting along with their delegations, including Clara Martinez-Alberola, head of Mr Juncker's cabinet, Gerard Kiely, head of the European Commission Representation in Ireland, legal adviser Michael Shotter and financial adviser Paulina Dejmek-Hack.