Jeremy Corbyn said results from the latest local elections show "a deal has to be done" on Brexit.
Asked about the figures so far, he said: "An arrangement has to be made. A deal has to be done. Parliament has to resolve this issue."
Mr Corbyn said there was a "huge impetus" on every MPs to find a way beyond the current logjam.
His comments came after shadow chancellor John McDonnell tweeted: "So far, message from local elections - 'Brexit - sort it'. Message received."
Despite some predictions Labour could pick up three-figure gains it is currently down more than 100 seats.
Though it did have the consolation of restoring control in Trafford for the first time since 2003.
So far the main opposition part has lost control in Darlington, Middlesbrough, Stockton and Wirral.
It also lost the mayoralty in Middlesbrough, where its vote was down 11% as independent Andy Preston was elected, although it did gain control of Amber Valley from Tories.
Both Conservative and Labour figureheads left no doubt that they saw the results as a demand for resolution of the Brexit impasse.
As Tory losses rose above 1,000, Theresa May claimed she had been expecting a "difficult election".
However, she said Brexit was "an added dimension" to that result.
She told Sky News: "These were always going to be difficult elections for us with us nine years into a government.
"Of course there is the added dimension we haven't got the Brexit deal over the line.
"But of course it wasn't a good night for Labour either - they were predicting they would make gains but they have lost over 100 seats.
"I think there has been a very clear message from people to both main parties that they want us to get on and deliver Brexit, so I welcome comments from Jeremy Corbyn that he thinks we should be working to ensure we can deliver a deal."
The party with the biggest surge in numbers has been the pro-EU Liberal Democrats.
It has gained more than 500 council seats to double its total, while The Green Party and independents also made gains in the races that focused on local issues such as garbage collection.
"Voters have sent a clear message that they no longer have confidence in the Conservatives, but they are also refusing to reward Labour while the party prevaricates on the big issue of the day: Brexit," said Liberal Democrat leader Vince Cable.
