WASHINGTON (CBS) — U.S. Senator Mark Kirk (R-Ill.) says he wants the U.S. to stand strong in the face of a new North Korean leader.

As WBBM Newsradio’s Jackie Swike reports, Kirk says the Korean Peninsula has been rendered unstable after Kim’s death on Saturday morning.

LISTEN: WBBM Newsradio’s Jackie Swike reports

“This is an attempt to pass power to a third generation of one family. But Kim Jong Un, the new leader, is only 29 years old, and the question tonight will be, is he maintaining the loyalty of key North Korean Army corps commanders, or will we have an unstable power struggle now in a heavily-armed North Korean state?” Kirk said in a telephone interview on the CBS 2 Morning News.

The key for the U.S. right now, Kirk said, is to maintain support for its South Korean ally, as President Barack Obama has affirmed.

“That’s the right move. Both the militaries, North and South Korea, are now on alert, and so it’s somewhat worrying that somebody could make a false move,” Kirk said. “President Obama was right to reaffirm our military alliance with the Republic of South Korea – remember, the United States just signed a big free trade agreement with South Korea as well. We have thousands of troops defending South Korea.”

But the U.S. should also make diplomatic efforts in North Korea, in hopes that relations with the country might improve at least to some degree.

“The funeral is now scheduled for the 28th of December, and if invited, the United States should send a high-level delegation, potentially as high as the vice president, to the funeral,” Kirk said, “and we would always like much better relations with North Korea, and with a brand new and very young leader – obviously his uncle will be making more decisions in the early days, but making a good impression could lower tensions quite a bit.”

The transition of power in North Korea will be far from orderly, Kirk explained.

“When (Kim’s) father took power in 1994, it was months of instability, and we’ve seen some instability again. Kim Jong Il – the recently deceased dictator – he started transitioning power to Kim Jong Un last year,” Kirk said. “We’ve had some military moves – even North Korea sank a South Korean naval vessel, probably in an attempt to look strong. That’s why we’re so concerned tonight about that and any other moves that the new leader makes to try to look tough to get the loyalty of the army behind him.”