Senator Ted Cruz has accused Barack Obama, the country’s first African American president, of having “inflamed racial tensions” during his time in the White House.

Cruz, a Texan who is running for the 2016 Republican presidential nomination, made the comments in a speech at a US Hispanic chamber of commerce event in Washington DC. The speech included other controversial assertions, including that the growth of national support for same-sex marriage was “heartbreaking” and that Democrats had tried to “scare” Hispanics into voting for them by talking about immigration.

Cruz said that Obama “could have chosen to be a leader” on race relations, but instead “has made decisions that I think have inflamed racial tensions – that have divided us rather than bringing us together”. Cruz also got in a dig at Vice-President Joe Biden, saying a comment Biden made during the 2012 presidential race had likewise detracted from racial comity.

Biden appeared in August 2012 before a largely African American crowd in Virginia and said Mitt Romney would be a bad choice for president. “He is going to let the big banks once again write their own rules, unchain Wall Street,” Biden said. “He is going to put y’all back in chains.” The Obama campaign declined to apologize for the comment.

Americans have become more focused on racial tensions during the Obama presidency, polls have found. Following the shooting death of Michael Brown in Ferguson, Missouri, in August 2014, the proportion of Americans naming “race relations” or “racism” as the top problem facing the country spiked to 13% in a Gallup poll, a 20-plus-year high.

Cruz placed blame for the phenomenon not on the seemingly constant high-profile cases in which unarmed black men have been killed by police officers since Eric Garner was killed in July 2014, but on the president.

Obama has faced the criticism before. Some supporters during his first presidential run said he was too slow to talk about race in light of incendiary comments by his former pastor, Jeremiah Wright. The candidate subsequently made a well-received speech in Philadelphia on the topic, which included the line: “But it is a story that has seared into my genetic makeup the idea that this nation is more than the sum of its parts – that out of many, we are truly one.”

In 2009 Obama said a white police officer had “acted stupidly” in arresting Henry Louis Gates Jr, the distinguished professor, on the porch of his own home. He later held a “beer summit” at the White House between Gates and the arresting officer, sergeant James Crowley.

Reflecting on the death of Trayvon Martin, the 17-year-old shot dead by George Zimmerman in Florida in 2012, Obama said: “You know, if I had a son, he’d look like Trayvon.” On Tuesday, Obama said that “since Ferguson” the country had “seen too many instances of what appears to be police officers interacting with individuals, primarily African Americans, often poor, in ways that raise troubling questions”.