In a speech at the party’s spring conference on Sunday, Sir Ed Davey said the home secretary’s response to the ‘humanitarian catastrophe’ has been ‘utterly shameful’.
Ms Patel and the Home Office have been approached for comment.
The Lib Dem leader said: ‘She has answered desperation with delays. Crisis with confusion. Pain with paperwork.
‘Friends, when we see parents and children, bombed out of their homes, journeying for days, in search of nothing more than a safe place to live, people across the UK have said loud and clear: we want to welcome them, with open arms. Just as we welcomed refugees of other conflicts in the past.
‘The British people want to offer them a home – but Priti Patel has slammed the door in their face.’
It came as the government announced details of a new scheme to help people fleeing the Russian invasion.
Levelling up secretary Michael Gove said ‘tens of thousands’ of refugees are potentially set to benefit from the new route, with the first expected to come the UK ‘in a week’s time’.
The government has been criticised over the speed and scale of its efforts to bring people fleeing the war to the UK, with access previously limited to those with family members settled in this country.
Earlier this week, Conservative MPs joined the Opposition in launching a furious attack on the Home Office’s response to the crisis.
On Tuesday, minister Kevin Foster confirmed 500 visas had been issued and the Ukraine family scheme had received more than 10,000 applications since its launch the previous Friday.
Mr Gove today said that ‘more than 3,000 visas’ have now been issued, up from the 1,305 figure given by Home Office minister Baroness Williams of Trafford on Friday, correct as of Thursday morning.
Sir Ed alleged that Ms Patel has shown ‘incompetence, indifference and sheer inhumanity’, which ‘does not befit our United Kingdom, with its proud history of providing sanctuary to those in need’.
‘Her inaction does not befit the British people, with all our compassion and generosity,’ he added.
‘It couldn’t be clearer that Priti Patel is not up to the job. The buck stops with the prime minister. So Boris Johnson must sack her, now.’
In a previous statement, the government said: ‘We are standing shoulder to shoulder with Ukrainians, which is why we’ve made it easier for those with valid Ukrainian passports to come here. This is alongside changes to visas to ensure Ukrainians in the UK can stay here.
‘We have expanded our visa application capacity to 13,000 a week, deployed additional staff across the EU, with a 24/7 helpline in place to ensure those who need appointments can get them to come here. This allows us to balance security risks while welcoming those in need.
‘A new sponsorship route, which will allow Ukrainians with no family ties to the UK to be sponsored to come here is also being brought forward and all the measures we’ve put in place follow extensive engagement with Ukrainian partners. We will keep our support under constant review.’