The official also emphasized that the briefings for Trump and Democratic presidential nominee Hillary Clinton "will be provided on an even-handed, non-partisan basis."
Trump's comments came at a wide-ranging news conference at his golf resort in Florida, where he downplayed his connections to Russia.
WikiLeaks release
U.S. computer experts have said in recent days they believe that Russian state actors are behind the hacking into computers at the Democratic National Committee headquarters in Washington, following WikiLeaks' release of nearly 20,000 emails that showed party officials favored Clinton's presidential nomination and tried to undermine the candidacy of her rival, Vermont Senator Bernie Sanders.
Some Democratic officials are claiming that the timing of the release of the documents, just before the Democratic National Convention convened this week to acclaim Clinton's nomination, suggests that Russian President Vladimir Putin favors Trump in November's U.S. national election to pick Obama's successor. Russia said it had nothing to do with the security breach.
Clinton, who claimed her party's 2016 nomination on Tuesday, said she considers the hacking to be a national security issue. The U.S. Federal Bureau of Investigation (FBI) is probing the breach.
No respect
Trump sought to distance himself from the purported Russian connection to the hacking at Democratic offices and Moscow's supposed support for his candidacy.
"It is so farfetched," he said. "It’s so ridiculous. Honestly I wish I had that power. I’d love to have that power, but Russia has no respect for our country."
Trump repeatedly said, "I have nothing to do with Russia,” although he had praised Putin in the past. "I have nothing to do with Russia. I said that Putin has much better leadership qualities than Obama, but who doesn’t know that?"
Clinton's use of the private email server, rather than a government server, has been a long-running controversy in the U.S., complicating her run for the White House. The FBI recently concluded that she was "extremely careless" in her handling of classified information in the emails during her time as secretary of state but that no criminal charges were warranted.