A joint statement issued by the families on Monday said Ling has a "serious medical condition'' that will be worsened by a sentence in a labour camp and that Lee has a four-year-old daughter who is beginning to worry about her mother.
'High stakes poker'
Meanwhile Bill Richardson, governor of the US state of New Mexico and a former US ambassador to the United Nations who has previously negotiated the release of Americans in North Korea, said on Monday that the Obama administration had contacted him for advice in the case and that he had also spoken to the women's families.
Richardson told US television channel NBC that political negotiations would now begin in a "high stakes poker game" for their release.
The two women, who were detained by North Korean border guards on March 17 and have been held in the country ever since were sentenced on Monday following a brief trial behind closed doors, the North's official Korean Central news agency (KCNA) said.
The journalists, who were working for California-based Current TV, an online and television service set up by Al Gore, the former US vice-president, cannot appeal because they were tried in the country's highest court, where decisions are final.
North Korea has said the two reporters had crossed illegally to its side of the border with China, although other reports have suggested the two were on the Chinese side when they were arrested.
Previous reports from North Korea have said Ling and Lee were accused of "hostile acts" but did not give details.
Analysts say the sentences appeared unusually harsh and seemed to back up views that the journalists could be used as a bargaining chip by the North in its standoff with the US.
Their arrest and trial come against a background of heightened tensions on the Korean peninsula, following the North's recent nuclear and missile tests.
|Laura Ling and Euna Lee have been sentenced to 12 years hard labour [EPA]
On Sunday Clinton said Washington was looking into putting North Korea back on a list of state sponsors of terrorism, a designation that could subject the impoverished state to more financial sanctions.
The US removed North Korea from the blacklist in October in a bid to revive faltering six-party nuclear disarmament talks, prompting the North to take some measures to disable its nuclear facilities.
But Pyongyang has since reversed those steps and said it had restarted its nuclear complex, including reprocessing nuclear fuel to obtain weapons-grade plutonium.
North Korea has also vowed to retaliate with "extreme" measures if the United Nations punished it for conducting its nuclear test last month.
The security council has been deliberating its response and may issue a new resolution as early as this week, although there appear to be division among members over how tough sanctions should be.
"Our response would be to consider sanctions against us as a declaration of war and answer it with extreme hardline measures," the North's official Rodong Sinmun newspaper said in a commentary on Monday.