In the statement, for the British prime ministers Mrs Theresa said ;
" We have no choice but to reach out across the House of Commons," the prime minister said.
"The referendum was not fought along party lines and people I speak to on the doorstep tell me they expect their politicians to work together when the national interest demands it."
Getting a majority of MPs to back a Brexit deal was the only way for the UK to leave the EU, Mrs May said.
"The longer this takes, the greater the risk of the UK never leaving at all."
May pointed that after doing "everything in my power" to persuade her own party - and their backers in Northern Ireland's DUP - to approve the deal she agreed with the EU last year, she "had to take a new approach".
Prime Minister Theresa May has insisted she had to reach out to Labour in a bid to deliver Brexit or risk letting it "slip through our fingers".
In a her statement on Saturday night, Mrs May explained there was a "stark choice" of either leaving the European Union with a deal or not leaving at all.
Some Conservatives have criticised her for seeking Labour's help after MPs rejected her Brexit plan three times.
Mrs May has written to European Council President Donald Tusk to request an extension to the Brexit process until 30 June but says if MPs agree a deal, the UK should be able to leave before European parliamentary elections are held on 23 May.
She says the UK would prepare to field candidates in May's European Parliament elections if MPs failed to back a deal.
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by the House of Commons.