Acting President Nicolas Maduro secured 50.8 percent of the vote in a win over opposition leader Henrique Capriles' 49 percent.
The British government issued a statement Friday saying it was looking forward to forging a deeper relationship with the Maduro government.
"We are concerned by reports of violence following the elections and call on all sides to work together to reduce tensions and to prevent further incidents," the statement added.
At least eight people died in political violence that followed Sunday's vote.
Capriles scored a partial victory when the country's National Electoral Agency said Thursday it would audit the vote sometime next week, The Wall Street Journal reports.
U.S. Secretary of State John Kerry testified before lawmakers this week that the U.S. government supported a recount. He said it was unclear if the U.S. government would formally recognize Maduro's victory.
Late Venezuelan President Hugo Chavez expressed annoyance with U.S. policies during his tenure. He died of cancer in March.
Maduro, who served as vice president during the Chavez administration, was quoted by Bloomberg News as saying he would "be a president with a firm hand."