A number of other parties have already announced their candidates and launched their European election campaigns, but the Conservatives have yet to do the same.
Theresa May brushed off renewed Tory calls for her to set a "road map" to resignation in the wake of disastrous council election results as Downing Street made clear the Prime Minister meant to see the first phase of Brexit through.
"She is here to deliver Brexit in phase one and then she will leave to make way for new leadership for phase two", the Downing Street spokesman said.
For months, Prime Minister Theresa May's government promised this election wouldn't be held in Britain, because the country would have left the European Union by now.
The chairman of the Conservative backbench 1922 Committee Sir Graham Brady, who met the Prime Minister privately on Tuesday, made clear she had not offered any further clarity about her future.
May has lost heavily on three attempts to get her Brexit deal through parliament.
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Earlier on Wednesday, May was confronted in the House of Commons by a Brexit-backing Conservative MP, Andrea Jenkyns, who said: "The public no longer trust her to run Brexit negotiations".
"It is of concern to me that our party's leaflet has failed to include that we will leave the customs union and the single market to ensure we can have an independent trade policy".
European elections on 23 May will go ahead, almost three years after the Brexit referendum, the government has confirmed.
The UK was originally due to leave the European Union on March 29, but as no deal was agreed by the British Parliament, the European Union extended the deadline to October 31.
May had been hoping that her deal or an alternative withdrawal agreement could be raced through the British Parliament to enable the voting in Britain to be cancelled.