But the government's refugee policy is coming under scrutiny after it was confirmed over the weekend that about 50 Ukrainians had been granted visas.
Boris Johnson said the UK would be "very generous" to refugees, but would not let people in without any checks.
It comes amid calls to do more than Russia's invasion of Ukraine continues.
Mr Johnson will discuss further sanctions against Russia with Canadian Prime Minister Justin Trudeau and Dutch Prime Minister Mark Rutte during their talks.
Later he will join a call with US President Joe Biden, French President Emmanuel Macron and German Chancellor Olaf Scholz.
During a visit to an RAF station with his fellow leaders, Mr Johnson said he was not sure about the accuracy of the 50 visas figure, but said the UK was "processing thousands".
The government has so far announced two main schemes for people fleeing Ukraine to come to the UK - one which allows family members of people settled in the UK to join them, and the other which allows organizations to sponsor a Ukrainian's entry.
He said the schemes were "very generous" but said Mr Putin was "doubling down on his aggression" and was attacking "in a pretty indiscriminate way" which would displace huge waves of people - adding that "we're going to have to respond to that".
Asked whether the government was considering a third option for refugees, Mr Johnson did not answer directly, but said the UK would not create a system "without any checks or any controls at all".
Home Office sources have said they are in the early stages of exploring a scheme to provide humanitarian access to people fleeing the conflict.
But a senior government source told the BBC the focus was still on the two schemes for Ukrainian refugees that have already been announced, and the need for further action was being kept under review.
The prime minister's official spokesman also insisted there were just two humanitarian options, with more details on the sponsorship route to be released later this week.
Labor leader Sir Keir Starmer said the Home Office was in a "complete mess" and the government must establish a "simple route to sanctuary", while Scotland's First Minister Nicola Sturgeon said the UK was "not doing anywhere near enough" to help refugees.
Ahead of talks with the other leaders, Mr Johnson said he thought there was more that could be done internationally to remove Russia from the Swift banking payment scheme.
The prime minister also said that with Mr Putin's "unrestrained" attacks on cities, there was more the world could do on sanctions, which was why the UK was bringing forward the Economic Crime Bill on Monday.
He added that "we want to go as fast as we possibly can" in imposing sanctions - with "nothing off the table".
More than 1.5 million people have fled Ukraine since the invasion began, according to the UN refugee agency.
As of Sunday, about 50 Ukrainians - less than 1% of the 5,535 people who have applied - had so far been granted visas under a scheme for refugees with family links to the UK, the Home Office said.
On Monday, there had been more than 10,000 applications from Ukrainians for visas, but No 10 was unable to say how many had been granted or rejected.
The UK has steadily increased its visa offer to refugees from the war, and Home Secretary Priti Patel said she was "doing everything possible" to speed up efforts to issue the travel permits.
Ukrainian cities have continued to suffer intense shelling, with officials saying Russian forces are targeting hospitals, nurseries and schools, and with residents caught up in the assault.
Russia says it will open up humanitarian corridors in several areas on Monday - after two previous attempts to evacuate civilians collapsed.
The corridor from Kyiv will lead to Russian ally Belarus, and civilians from Kharkiv will only have a corridor leading to Russia. Corridors from the cities of Mariupol and Sump will lead both to other Ukrainian cities and to Russia, the AFP news agency reports.
Peace talks have resumed between the two sides in Belarus, and their respective foreign ministers will meet in Turkey.
Meanwhile, MPs are expected to vote later on the Economic Crime Bill, which aims to make it easier to sanction individuals.
In recent days, the government has announced asset freezes and travel bans on a number of oligarchs - but has faced accusations of being too slow to sanction those with links to President Putin.
The bill will set up a new register that will mean foreign owners of UK property must declare and verify their identities with Companies House.
In addition, new measures will provide UK authorities with more time to carry out investigations, as well as giving them protection from prohibitive legal costs.
MPs are expected to vote through all stages of the bill in a single sitting.
You must be logged in to post a comment.