As special counsel Robert Mueller's Russia investigation pushes ahead, New Jersey Gov. and frequent Trump ally Chris Christie says "no one" has told President Trump he is under investigation as part of the probe.

"I would say the important thing about today for the American people to know is the president is not under investigation," Christie said, although he didn't explain how he knows this information. "And no one has told him that he is. He's been cooperating fully with the special counsel's office. And if the special counsel feels as if now, along with the grand jury, there's actions to take against some folks, that's the special counsel's job."

The federal grand jury being used by Mueller in the investigation into Russian meddling in the 2016 presidential election has approved the first charges stemming from the investigation, sources told CBS News. The indictment is currently under seal but is expected to become public as early as Monday. The nature of the charges, and the identity or number of individuals targeted, are unclear. CNN first reported the approved charges Friday night.

Christie, who is a former federal prosecutor, said that alleged "leaking" of Mueller's grand jury activity was "absolutely against the law."

"There are strict laws against any of this type of leaking of grand jury activity," Christie said Sunday on CBS News' "Face the Nation." "And so, you know, the idea that we may know in fact that there has been some activity done already depending upon who leaked that information, that could be a -- that could be a criminal violation as well. So we have to be very careful about this stuff."

"Grand jury secrecy is very important to the effectiveness of a grand jury investigation," he added.

Meanwhile, Christie, who chairs the president's opioid commission, said criticism of Mr. Trump's recent response to the crisis has been "totally misplaced." On Thursday, Mr. Trump declared the crisis a public health emergency.

"We recommended in our first commission report that he use either the Public Health Safety Act or the Stafford Act to be able to declare a national emergency," Christie said. "He did that under the Public Health Safety Act. Now it is incumbent upon Congress to be able to appropriate money into the public health emergency fund. There's only $57,000 there right now. Nothing the president can do about that. Congress appropriates."

The governor said he believes bipartisan members of Congress will act swiftly to allocate funds to combat the crisis urgently.

"They're going to react to this emergency like they've reacted to funding Puerto Rico, funding Texas," Christie said.

Christie said he is pleased with the approach the president has taken so far, saying he is "proud" of Mr. Trump, following the president's Thursday announcement.

"This week we'll bring him a final report with even more recommendations on how to deal with this problem. We have to stop our people from dying. And I know the president's committed to this," Christie said.