"China called last night our top trade people and said 'let's get back to the table' so we'll be getting back to the table," Trump said during a meeting with his Egyptian counterpart Abdel Fattah el-Sisi on the sidelines of the G7 summit here.
"So I think they want to do something, they've been hurt very badly but they understand that this is the right thing to do and I have great respect for them. This is a very positive development for the world."
China was yet to comment but earlier called for "calm" to resolve the row.
Trump said that Chinese officials made two "very, very good calls" on Sunday night and that Beijing wanted to "make a deal". The US President added that he respected his Chinese counterpart Xi Jinping for taking this initiative.
Both nations have been embroiled in a tit-for-tat trade dispute that has escalated through tariffs.
Earlier on Monday Asian stock markets tumbled over concerns about the trade war, with Hong Kong's Hang Seng index losing more than 3 per cent before regaining ground.
However, European shares climbed after Trump's more conciliatory comments and US markets opened between 0.7 per cent and 1 per cent higher, having fallen sharply last week.
Trump announced fresh tariffs on Friday after China unveiled plans to slap duties on $75 billion of US products.
The President said he had instructed American companies to look for alternatives to China.
The trade war, largely centred over steel and aluminium in the beginning, has since expanded to included various sectors including agriculture.
Trump has also targeted China for its alleged theft of intellectual property.
( With inputs from IANS )