Gordon Johndroe, a White House spokesman, said after Monday's summit: "Both leaders agreed that in negotiations for the release, there should be no quid pro quo for the hostages."
"The Taliban are brutal and should not be emboldened by this," Johndroe said.
But families of the hostages gathered in at a church on the outskirts of Seoul and criticised the summit for not doing enough to help secure their release.
Relatives wore paper signs that read "send them home" and "set them free" while a spokesman read a statement on television.
"We could not sleep at night due to our expectations, as the release and safe return of our families depended on the two leaders' summit," the statement said.
"But the summit, which failed to concretely touch on the families detained in Afghanistan, made insufficient effort to actively save precious lives."
The Taliban has been demanding the release of captured fighters in return for the freedom of the 18 women and three men who were taken on July 19 while travelling in southern Afghanistan.
Two male hostages have been shot dead by the group and it has threatened to kill the rest if their demands are not met.
South Korea's foreign minister has dismissed Taliban claims that two of the female hostages were seriously ill.
"The hostages can't be perfectly healthy after nearly 20 days in captivity," the ministry quoted Song Min-soon as saying.
He said: "There are no signs of health problems that could pose a threat to their safety."
"The government is making various efforts for the release of the hostages."
A team of South Korean diplomats has been sent to Afghanistan to negotiate with the Taliban but a date and venue for talks are still to be arranged.
Source: Al Jazeera and agencies