While visiting the nation's capital on his last stop of a four-nation trip of Europe, Mr. Clinton offered Ukraine a strategic partnership including financial aid to help shut down what's left of the infamous power plant, CBS News Correspondent Bill Plante reports.
Mr. Clinton's brief visit Monday followed a two-day summit in Moscow with new Russian President Vladimir Putin. Upon arriving in Kiev, the president headed for a welcoming ceremony with Kuchma.
"This is a hopeful moment. It is also a moment when we remember those who suffered as a result of the accident there," Mr. Clinton said Monday.
Mr. Clinton said the U.S. would provide $78 million to help efforts to contain radiation at the troubled plant, and $2 million for safety measures at other nuclear power plants in Ukraine.
On Sunday, Kuchma called Mr. Clinton's six-hour visit - the last stop on his seven-day European tour "a highly symbolic event for the country" that highlights its democratic achievements. U.S. and Ukrainian officials said Chernobyl was a focal point of the formal meeting.
"This reactor must be stopped from all points of view, and first of all from the point of view of security. I have no doubts about that," Kuchma said Sunday.
He also said, however, "We won't be able to deal with this serious problem alone." Kiev, he indicated, wanted Mr. Clinton to promise a contribution to a replacement reactor project.
Kuchma has repeatedly delayed Chernobyl's closure, saying Ukraine hasn't gotten much-needed Western aid promised to finish construction of two new reactors at the Rivne and Khmelnitsky nuclear plants in exchange.
The cost of the new reactors has been estimated $1.2 billion.
The U.S plans to provide some funding for repairs on the leaky concrete and steel sarcophagus covering Chernobyl's reactor No. 4, ruined in the April 1986 accident, according to American Ambassador Steven Pifer.
Ukraine, Belarus and Russia still spend huge sums cleaning up the aftermath of the fire and explosion that spewed radioactivity across Europe and contaminated large areas.
In mid-May officials at the nuclear plant denied charges by a U.S. official that anything was wrong at the plant, even as forest fires spread the remnants of radiation from a 1986 disaster at facility.
The denial came in response to a claim by an unidentified U.S. official that a malfunction has forced officials at the plant to cut power back 50 percent.
According to the U.S. official, the new malfunction caused a turbo generator in the reactor to switch off, leaving only one reactor was in operation.
The U.S. official said there is no evidence of radiation as a result of the malfunction, and the probledoes not seem to be serious.
But, at the same time, the official said, forest fires in the area has caused the circulation into the air of remnants of radiation in roots and stems of plants, with the result that the radiation level in Kiev was elevated slightly.
In Kiev, officials denied that the power had been cut back by half. Plant duty officer Andriy Bilyk said: "This is complete nonsense. There are no problems. The reactor is working in a normal regime."
A cover for the plant was built after the disaster, but it is considered unstable. Some $360 million, in addition to $400 million already raised, is needed for the new cover.
The Chernobyl disaster caused an estimated 4,000 deaths among those who took part in the cleanup, and 70,000 people were disabled by radiation, according to Ukrainian government data.
Malfunctions are frequent at nuclear power plants in the former Soviet Union, including the one at Chernobyl, and that forced a temporary halt or reduction of output. Most do not release radiation and are quickly repaired.
There were four completed reactors at Chernobyl. One was destroyed in the 1986 explosion, one was damaged in a fire in 1991 and one was closed subsequently, leaving only one in operation.