"FBI is leading this investigation, which is still in its early stages," Biden said. "We don't yet have any information about the motive of the shooter. We know who he is. I urge everyone, everyone, please don't make assumptions about his motives or his affiliations."
Biden added that he had spoken with Republican presumptive candidate Donald Trump after the unsuccessful attempt on his life on Saturday night and that the two men had a good conversation.
"Last night I spoke with Donald Trump: I'm glad he is recovering," Biden said in a nationally transmitted broadcast. "We had a short but good conversation."
Biden noted that he had directed the US Secret Service to review all security measures in place for the Republican National Convention in Milwaukee this week following the failed assassination attempt against the presumptive Republican nominee Donald Trump.
"I've directed the head of the Secret Service to review all security measures for all security measures for the Republican National Convention, which is scheduled to start tomorrow," Biden told reporters.
"I've directed an independent review of the national security at yesterday's rally to assess exactly what happened, and we'll share the results of that independent review with the American people as well."
Biden added that Trump as a former US president and nominee of the Republican Party already receives a heightened level of security and he has consistently ensured that the US Secret Service provides him with every resource, capability and protective measure necessary to ensure his continued safety.
On Saturday evening, shots were fired during Trump's campaign event in Pennsylvania. The ex-president sustained a gun wound to his right ear and was briefly hospitalized. The shooter killed an audience member and critically injured two others in the crowd before the US Secret Service neutralized him. The FBI is investigating the incident as an assassination attempt.
The gunman was identified as 20-year-old Thomas Matthew Crooks of Bethel Park, Pennsylvania, according to the FBI.