China said last month a joint declaration with Britain over Hong Kong, which laid the blueprint over how the city would be ruled after its return to China in 1997, was a historical document that no longer had any practical significance.
In response, Britain said the declaration remained in force and was a legally valid treaty to which it was committed to upholding.
China says no foreign country has a right to get involved with Hong Kong as it is an internal affair for China, and has also reacted angrily to six-monthly reports the British government gives to Parliament about Hong Kong.
Meeting on the sidelines of the G20 summit in the German city of Hamburg on Friday, Xi told May that bilateral relations should be cultivated on the basis of "consolidating strategic mutual trust", China's foreign ministry said on Saturday.
"Both sides should uphold the principle of mutual respect and equality, and respect each other's core interests and major concerns," the ministry cited Xi as saying.
"Both sides must seek common ground while shelving differences."
On Wednesday, British Minister of State for Asia and the Pacific Mark Field met Chinese ambassador Liu Xiaoming in London and made clear Britain's commitment to the joint declaration, Britain's Foreign Office said.
"This declaration, registered with the UN, remains in force until July 2047. As a consequence, the minister did not accept the Chinese government's position that this was purely an historical document," the Foreign Office said.
While China and Britain have a history of disputes over human rights and the future of Hong Kong, ties have warmed in the past few years and economic links have grown in what both countries call a "golden age", though Britain upset China last year by putting on hold a nuclear project it later approved.
China is high on Britain's list of countries with which to sign a free trade deal once Britain leaves the European Union.
Xi told May that the two countries should deepen cooperation in the finance and nuclear energy sectors, China's foreign ministry added, without giving details.