Negotiators at G-20 talks in Hamburg, Germany, are working on a final statement, with climate change as the only outstanding issue, officials say.
They say a joint position on trade has been agreed, with all countries pledging to resist protectionism.
Meanwhile leaders have held separate talks. President Donald Trump met British PM Theresa May, and said a US-UK trade deal would be signed soon.
The final talks come after a second night of violent protests in Hamburg.
Negotiators worked through the night in an attempt to reach a compromise on the wording of the summit statement – which is expected later on Saturday.
The host, German Chancellor Angela Merkel, held a working breakfast with Presidents Putin of Russia and Macron of France. On Friday had described the first day of talks as “very difficult”.
But early on Saturday, an EU official told Reuters news agency: “The outcome is good. We have a communiqué. There is just one outstanding issue on climate.” He added that the statement included a pledge to “fight protectionism”.
Mr Trump, after his morning meeting with Ms May, said he expected a “very powerful” trade deal between the two countries “very quickly”.
Trump: UK-US trade deal to happen quickly
The G20 (Group of Twenty) is a summit for 19 countries, both developed and developing, plus the EU.
What about those ‘difficult’ issues?
Leaders at the summit have been struggling to find common ground with the US following President Donald Trump’s decision to withdraw from the Paris climate agreement last month.
One unresolved section of the G20 communiqué is linked to the US desire to have a reference to fossil fuels – according to reports quoting unnamed EU officials.
A separate issue is trade – although Mr Trump has said that he is not opposed to trade in principle, his position is that any trade deals agreed have to protect US industry.
Mrs Merkel said on Friday: “The discussions are very difficult, I don’t want to talk around that.”
She added that she hoped that the differences with the US would not affect the commitments made by other nations.
Why do parts of Hamburg resemble a war zone?
Mrs Merkel’s comments came amid large protests on the streets of Hamburg, with demonstrators and armed police clashing into the early hours of Saturday.
Demonstrators – who were protesting against the presence of Mr Trump and Mr Putin, climate change and global wealth inequalities – set fire to vehicles and barricades, threw rocks at officers and looted shops.
At one point, police chased protesters across rooftops while officers on the streets used water cannon on protesters.
Nearly 200 police officers were injured during the protests. Dozens of protesters have been detained.
What happened when Trump met Putin?
On Friday, Mr Trump used his first meeting with Russian President Vladimir Putin on the sidelines of the G20 to discuss the alleged Russian hacking of last year’s US presidential election.
Both sides called the meeting positive – but differed in their descriptions of the hacking discussion.
Russian Foreign Minister Sergei Lavrov said “President Trump said he heard clear statements… that Russian authorities did not intervene [in the US election], and he accepted these declarations.”
However, US Secretary of State Rex Tillerson said Mr Trump “opened the meeting with President Putin by raising the concerns of the American people regarding Russian interference in the 2016 election.
“They had a very robust and lengthy exchange on the subject. The president pressed President Putin on more than one occasion regarding Russian involvement.”
He said it was not clear whether the two countries would ever come to an agreement on what happened.
Other topics discussed during their meeting included the war in Syria, terrorism and cybersecurity.