The decision came in the first session on Thursday of the new trial that Libya's Supreme Court ordered late last year after it overturned death sentences handed down against the six in 2004.
Judge Mahmoud Huwaissa, the presiding judge on a three-member tribunal, rejected the request for bail after the prosecutor argued that the defendants might try to flee from the country.
The prosecutor added that one had already attempted to escape from prison, but he did not elaborate.
Thursday's brief session at a Tripoli criminal court, attended by the six defendants, dealt with procedural matters.
Huwaissa adjourned the trial to June 13.
Treatment of accused
Ashraf al-Hazouz, the Palestinian doctor, told The Associated Press in the courtroom that "we are also victims like those children, but we hope that this tragedy will end soon".
Al-Hazouz also said he had not been allowed to speak to his family for the past five months, and said he wanted to receive the same treatment as the Bulgarian nurses, implying they enjoyed privileges not given to him.
Victims' families demand
The six have been in Libyan custody since 1999.
The 426 children were said to have been infected with HIV, the virus that causes Aids, at a hospital in the Libyan city of Benghazi, as part of an alleged experiment to find a cure for the disease.
Europe, the US and human-rights groups have accused Libyan authorities of blaming the defendants for poor hygiene that they say caused the infections.
The medical workers first stood trial in 2004.
About 50 of the children have died, and the case has fuelled outrage among the families of the victims.
Tripoli has suggested that the nurses could go free if money were provided to cover financial compensation for the families of the victims and medical treatment for the children.
The victims' families have demanded 4.4 billion euro ($5.43 billion) from a group of international donors trying to settle the dispute, although Bulgaria has refused to pay any compensation, saying it would be a recognition of guilt.
But the US, EU, Libya and Bulgaria have agreed to back the formation of an aid fund, and are seeking ways to help the victims and their families.
The convictions have become a major sticking point to Libya's efforts to emerge from decades of diplomatic isolation.