There must be no “safe spaces” for terrorist funding in the global financial system, Theresa May will tell a meeting of the G20 on Friday.
The UK PM will focus on ways to track small sums of money used to finance “lone wolf” attacks, as well as large transfers, at the summit in Germany.
More must also be done to tackle the risk of foreign fighters “dispersing” from Iraq and Syria, she says.
The terror threat must be combated “from every angle”, Mrs May is urging.
The UK has been hit by attacks in London and Manchester in recent months.
Ahead of the summit in Hamburg, Mrs May said the terrorist threat was “evolving”.
“We have seen the threat spread out of Syria and Iraq – into other countries and online.
“As we deny physical space to terrorists to operate in theatre, we must outpace the terrorist methodology as it develops to attack other vulnerable targets and increases inspired attacks.
“We must therefore combat the threat from every angle.
“This includes taking measures against permissive environments for terrorist financing, and monitoring the dispersal of foreign fighters from battle.”
Police and protesters have clashed in Hamburg, where the G20 meeting of world leaders begins on Friday.
Police fired water cannon at a march attended by thousands carrying banners with slogans such as “Welcome to hell” and “Smash G20” on Thursday.
Up to 100,000 protesters are expected in Hamburg during the summit.
Mrs May will address the summit in the wake of attacks in Westminster, Manchester, London Bridge and Finsbury Park in the past few months.
In May, she urged world leaders at a G7 summit to do more to combat online extremism.
On Friday, she will say that loopholes being exploited by so-called Islamic State and other terror groups in financial systems must be closed.
New technology and partnerships could help banks and financial technology companies to spot suspicious small transfers of cash, she will say, which are hard to identify but must be challenged.
And she will press the need for better information sharing about people known to have travelled to fight in IS-controlled territory – to track them if they attempt to return to their home countries.
US President Donald Trump met German Chancellor Angela Merkel on Thursday and the pair spent an hour talking about North Korea, the Middle East, the conflict in eastern Ukraine and G20 issues, a German government spokesman said.
Trump meets Putin
Last week Mrs Merkel said the G20 would focus on the Paris climate deal, which the US has withdrawn from.
However, she has since said that as the G20 host, she would work to find compromises.
A UK government official said Mrs May was expected to raise climate change with the US president at the G20, and would stress that Britain “remains fully committed” to the agreement.
The summit will also see Mr Trump meet Russian President Vladimir Putin for the first time. The meeting will take place at 14:45 local time (13:45 GMT) and last for an hour, Russian media report.
On Thursday Mr Trump used a speech in the Polish capital Warsaw to call on Russia to stop “destabilising” Ukraine and other countries.