"Other Israeli astronauts will be sent into orbit," Mr Sharon told a cabinet meeting attended by US ambassador Dan Kurtzer, on Sunday.
"These seven astronauts paid the price for man's conquest of space... and the world salutes these heroes," he said.
Flags flew at half mast outside government buildings in Israel, as the country mourned the loss of Colonel Ramon and his fellow astronauts.
Israeli Defence Minister Shaul Mofaz said Israel would continue to participate with the United States in its space programme.
Colonel Ramon's father, Eliezer Wolferman, and his brother, Gadi, were being flown to the United States to be close to the astronaut's wife, Rona, and their four small children.
Non-stop coverage
News that Nasa had lost communication with the shuttle came just before the end of the Jewish Sabbath.
Israel's Channel Two television had been interviewing Mr Wolferman live shortly before the scheduled landing.
After breaking away to a correspondent in Florida, the station's anchorman explained that Mr Wolferman, 79, had been taken away from the studio.
Word of the tragedy spread quickly.
Israel's television channels carried non-stop coverage of the unfolding disaster and groups of Israelis gathered around television and radio sets to hear the latest news.
"This was a dream come true for Ilan," Colonel Ramon's brother told Israeli television, in tears.
"He wrote me e-mails from the shuttle and was literally on cloud nine," he added.
National hero
Colonel Ramon's death is being treated as a national tragedy in Israel.
"
This is going to hit Israelis quite hard because it is very personal
"
Ricky Ben-Or, Israeli
The launch made the front pages of every Israeli newspaper, prompting headlines such as "Fly, Ramon, cut through the skies," "A great step for Israel," and "Touching the sky."
Israelis are now mourning the death of a national hero.
Many saw Colonel Ramon as a symbol of optimism after more than two years of conflict with the Palestinians.
"It's terrible because Israelis, my kids in school for instance, have been studying about space and the Israeli astronaut Ilan," said Jerusalem resident Ricky Ben-Or.
"We are a very depressed country at the moment. This is going to hit Israelis quite hard because it is very personal," he added.
"It was a celebration for the country and it is ending so tragically," said Hezi Yitzhaki of Tel Aviv.
"An entire country was so proud of him. We are already in such a bad state."