Theresa May will not be asking the EU for a long delay when she formally requests that Brexit is postponed.
Downing Street said the PM shared the public’s “frustration” at Parliament’s “failure to take a decision”.
BBC assistant political editor Norman Smith said the delay would not be beyond the end of June.
A cabinet minister has told the BBC this would be the “wrong choice” and a “craven surrender to hardliners” within the Conservative Party.
Under current law, the UK will leave the EU – with or without a deal – in nine days.
The PM is due to send a letter requesting a delay to Brexit later, ahead of a EU summit on Thursday at which she will discuss the matter with fellow leaders.
Any delay will have to be agreed by all 27 EU member states and EU Brexit negotiator Michel Barnier has said the EU will not grant it without a “concrete plan” from the UK about what they would do with it.
When her letter to the EU actually emerges, the final wording will be key – will she rule out ever seeking a longer delay?
Will the text be clear that if Parliament fails to meet its second deadline then the PM will argue for leaving without a deal done? Ultimately, remember, the decision on the length and conditions attached is down to the EU, not the UK.
But as things stand, the prime minister seems to be ratcheting up the pressure for the next few weeks in the hope of pushing her deal through a reluctant Parliament, rather than accepting that the dilemma and level of disagreement is so profound, that a longer rethink might be what is required.
It comes after MPs rejected the withdrawal deal Mrs May has negotiated with the EU for a second time last week by 149 votes. They also voted in favour of ruling out leaving the EU without a deal, and in favour of extending the Brexit process.
The prime minister had hoped to have a third attempt at getting MPs to back her deal – but Speaker John Bercow effectively torpedoed that with his surprise intervention.
He said a third “meaningful vote” could not happen in the coming days if it was “substantially the same” motion.
Education Secretary Damian Hinds told the BBC that MPs had to “get on with” approving a Brexit deal – although he said another vote would not take place until ministers had “some confidence” of victory.
“You can’t keep on kicking the ball further and further down the street,” he told Radio 4’s Today. “You have to pick up and run with it.”
But an unnamed cabinet colleague told the BBC that asking for such a short delay was “weak, weak, weak”.
“This substantially increases the risk of no deal,” they said. “Her most craven surrender to the hardliners yet. She knows this is the wrong choice for the country but she’s putting her short term interests first.”