Remain-supporting parties should discuss working together in a snap general election or second EU referendum, Plaid Cymru's leader said.
Adam Price has written to the Liberal Democrats, Green Party, Change UK and the SNP.
He said they should work together for "as long as necessary" to deliver another vote on EU membership.
His call comes after the Brexit Party took two Welsh seats in the recent EU elections.
Plaid Cymru and Labour each took one of the country's four MEP seats in Brussels.
Despite the Brexit Party's victory, Mr Price said the combined total votes given to anti-Brexit parties shows that Brexit "cannot be considered the settled will of the people".
The Brexit Party gained 32.5% of the vote in Wales with UKIP taking 3.3% while Plaid Cymru received 19.6%, the Liberal Democrats 13.6%, Green Party 6.3% and Change UK 2.9%.
"With the Brexit Party having won the highest number of seats, there is now a grave risk that the result will be used to justify a no-deal Brexit," Mr Price said.
"I am particularly concerned that it will be used to influence the candidates running to become the next leader of the Conservative Party."
He described an "urgent need" for the parties to work together to "ensure that all the nations of these islands are not dragged headfirst towards a no deal Brexit for which there is no mandate".
Mr Price added: "We are passionately pro-European parties who believe that our nations' rightful place is at the heart of Europe.
"We must not let the politics of the Brexit Party divide us as we seek to maintain our nations' place in Europe."
Mr Price invited fellow leaders to meet him for an "initial, exploratory" discussion.
A Welsh Liberal Democrat spokesman said the party was always happy to discuss ways of achieving "our common aims".
He added: "Since June 2016, Liberal Democrats have led efforts in Parliament to secure a people's vote, and this has included work with other parties with varying degrees of success.
"We've done this because Remainers expect us to work together where necessary to deliver a People's Vote."
Change UK MP Chris Leslie said the party remains ready to continue working with other parties, including Plaid, to "prevent a disastrous no-deal Brexit".
He added that Change UK has "already engaged in an unprecedented level of cross-party cooperation since we formed".
The Green Party and the SNP have been asked to comment.