Jailed activist Jestina Mukoko was taken to a clinic for treatment
Zimbabwe's new PM Morgan Tsvangirai spent his first full day in office visiting political prisoners he wants to see freed from a jail near Harare.
The prisoners were given no promises of release, but the prime minister told them their cases would be processed more quickly, his spokesman said.
Mr Tsvangirai was sworn in as PM on Wednesday by long-time rival President Robert Mugabe.
Their coalition government's cabinet is due to be sworn in on Friday.
However, Mr Mugabe has not yet revealed his choices for the portfolios set aside for his Zanu-PF party under the power-sharing accord.
Mr Tsvangirai said in a speech after his inauguration ceremony that he wanted political prisoners freed immediately.
His spokesman, Joseph Mungwari, said the prime minister spent 45 minutes with 16 prisoners linked to his Movement for Democratic Change (MDC) party on Thursday.
They have been accused of subversion and recruiting fighters to overthrow Mr Mugabe - charges denied by the MDC.
No assurances of release were obtained during the visit to the maximum-security prison near Harare, Mr Mungwari said.
Mr Tsvangirai told a rally in Harare he wanted political prisoners freed
However, Mr Tsvangirai said later that the cases would be expedited and the law would take its course.
After Mr Tsvangirai's visit, three other detainees, including Jestina Mukoko, a prominent human rights activist held since December, were taken from prison for medical examinations at a private clinic in Harare, their lawyers told the AP news agency.
Irene Petras, head of the Zimbabwe Lawyers for Human Rights, said the three needed urgent hospitalisation.
Mr Tsvangirai had earlier said he would refuse to become prime minister until his jailed supporters and activists were freed.
Trade union meeting
Also on Thursday, Mr Tsvangirai held talks with leaders of the Zimbabwe Congress of Trade Unions (ZCTU).
The group - along with other independent organisations - had wanted fresh elections rather than power-sharing.
ZCTU president Lovemore Matombo said labour groups saw the unity government as a "transitional arrangement" leading to fresh, free and fair elections.
"We shall see how it works," he said, adding that workers would strike if they were not satisfied with the Tsvangirai-Mugabe government.
Mr Mugabe, who has ruled Zimbabwe for 28 years, has promised to co-operate in the unity government.
Correspondents say the fate of political prisoners will be seen as a test of whether the two men's parties can work together.
Analysts say that although Mr Mugabe has yet to appoint his party's ministers, the new unity government seems certain to create strange bedfellows with MDC members working alongside their former Zanu-PF adversaries.
A final deal on power-sharing was reached in January, after Mr Tsvangirai returned to Zimbabwe following an absence of more than two months for fresh talks with Mr Mugabe.
Zimbabwe faces rampant inflation, a cholera epidemic and at least 90% unemployment.