Hundreds of people gathered for a vigil to support Ukraine on Ipswich Cornhill on Wednesday.
Suffolk's MPs have called for the UK to show compassion and cut bureaucracy surrounding visa applications for Ukrainian nationals.
On Thursday home secretary Priti Patel promised a streamlined online visa application system for Ukrainians seeking to flee the war with Russia in response to criticism of her approach to the crisis.
Visas are currently available to relatives of people who live in the UK. Another promised route, allowing individuals and companies to sponsor Ukrainians to come to the UK, has yet to be established.
From Tuesday, Ukrainians with passports will no longer need to go to a visa application centre to give their biometrics before they come to the UK.
But Suffolk MPs called on the government to slash bureaucracy and show compassion in helping Ukrainians fleeing the conflict.
Peter Aldous, Waveney MP, said: "The daily reports of the emerging humanitarian crisis in Ukraine are alarming, many constituents are contacting me expressing their upset and some are being incredibly generous in offering to open up their homes to those who are being forced to flee their own homes.
"There is a need to ensure that there is an effective and accessible system that enables Ukrainian refugees to come to the UK.
"While the Home Office has quickly put in place a framework that includes the expanded Ukrainian Family Scheme and the Local Sponsorship Scheme for Ukraine, there is a concern that these routes are too bureaucratic and are not yet working well or quickly enough.
"As we are doing with the provision of military defence and welfare assistance on the ground in Ukraine, it is important that Britain provides leadership in supporting those who are being forced to flee their homeland."
Ipswich MP Tom Hunt said accepting refugees would present challenges for councils, but it was "quite simply the right thing to do".
He said: "I am – like all of the constituents who have contacted me about this issue – very keen for us to move and move in quite a big way to show the compassionate spirit of this country and to provide a safe haven for a significant number of Ukrainian people who are fleeing this warzone.
"But we do also have to realise that this is going to present a significant challenge to us as a country and to local councils up and down the country.
"It's a challenge that I believe that we have to meet. And it's one that I believe that we should meet for humanitarian reasons, and because it is quite simply the right thing to do. But I think it is one that we're going to have to be prepared for."
South Suffolk MP James Cartlidge said the UK's role in the conflict needed to extend beyond just supporting refugees.
He said: "Of course, welcoming refugees is very important and so I was pleased that the Home Secretary confirmed we will be streamlining our procedures for those wishing to come to the UK from Ukraine.
"Nevertheless, the most urgent and pressing task is to tackle the cause of the crisis – Putin’s aggression, so horrifically manifested in the maternity hospital bombing atrocity.
"While there is not likely to be any quick resolution, our role in arming the Ukrainian military has been significant, with what seems to be a demonstrable impact on the battlefield.
"We confirmed this week further steps to provide significant defensive military capability and, combined with our role in driving international financial restrictions that are throttling Putin’s economy, we are making a real difference.
"But there is a hard road ahead, and there will be impact at home, as we are seeing in rising prices for fuel. We must hold our nerve and continue to do everything possible to support the brave people of Ukraine."
Dr Dan Poulter, MP for Central Suffolk and North Ipswich, said: "Britain has a long and proud history of accepting refugees, most notably during the time of Nazi Germany but we also played a part in accepting refugees from Afghanistan.
"It's right that we support those Ukrainians who come to seek refuge here.
"The challenge in these situations is always supporting timely entry to the UK. But inevitably, there has to be some level of check to make sure that people are making valid claims.
"It's very difficult to do and at a time of great human suffering you need to have an asylum system that is compassionate – that mustn't be lost."
All seven Suffolk MPs were contacted for comment.
Published by the East Anglian Daily Times.