Theresa May is to urge China to stop flooding the market with cheap steel in talks with its president at the G20.
The UK's steel industry has been devastated by a wave of cheap Chinese exports.
The Prime Minister will say "increased action" is needed to reduce over-capacity when she meets President Xi Jinping on the sidelines of the two-day summit in Hamburg, a senior Number 10 official said.
Mrs May will also repeat her call for China to do more to stop North Korea's missile testing programme.
Beijing is facing widespread international pressure to use its influence over its ally following the latest launch.
Protesters have set fire to cars and tried to block delegations from entering the summit as part of a wave of anti-capitalist demonstrations.
More than 100 police were injured in clashes on Thursday evening and water cannons have been used to control the activists.
Mrs May led demands on Friday morning for an international effort to tackle terror funding as G20 leaders gathered for the first session of the summit.
Action must be taken to choke off the funding for terrorists that is being funnelled through international financial institutions, she said.
The premier was given a prime spot at the table as leaders gathered for a working lunch, seated near host, German Chancellor Angela Merkel, and next to Donald Trump.
Mrs May will meet the US President for talks on Saturday morning, where she will raise concerns over his decision to pull America out of the Paris Agreement on climate change.
The PM said she hopes President Trump will take America back into the international deal.
"I will be making that message," she told ITV News. "I will continue to give the message that the United Kingdom believes in the importance of the Paris Agreement."
On Saturday afternoon, she will meet Turkey's Recep Tayyip Erdogan to discuss counter-terrorism.
Mrs May is being accompanied by husband Philip - his first official overseas visit. He is joining other spouses for a separate programme of events, which includes a river boat trip through the port city.
But he will join the Prime Minister for a concert at the Elbphilharmonie concert hall on Friday night, where Beethoven's Symphony No 9 will be played, which includes the melody for the EU's anthem.
As well as tackling terrorism, Mrs May has three other key priorities for the summit.
She will push for action to create an "orderly" migration by ensuring refugees claim protection in the first safe country they reach, improving distinction between economic migrants and refugees and the right of all countries to control their borders.
She also wants G20 countries to work together to meet UN targets to wipe out modern slavery by 2030.
Amid fears of growing protectionism following President Trump's America First policy, the Prime Minister will also call for a continued commitment to free trade and action to encourage greater corporate responsibility.