The demands followed a week of protests and clashes with police that left at least 43 people dead, according to a leading human rights group.
In a bid to calm the situation, 72-year-old veteran leader Ortega has agreed to hold talks, but the framework has not yet been defined.
The students told a news conference in Managua that their demands must be met for them to take part.
The conditions included police involved in the repression being fired, an independent UN-backed body being established to investigate the violence, that relatives of those killed be included, and that the talks be held in public.
Any body investigating the violence must be “independent and credible” and have international backing to carry out its work, which would involve “investigating, condemning and sanctioning all those responsible for both approving and committing” the violence, they said.
The call came a day after Human Rights Watch called for pressure to be put on Ortega’s government to allow a visit by Inter-American Commission of Human Rights, the main rights body in the Americas, to investigate the allegations of abuse.
The students also demanded a “Truth Commission” created by the government be disbanded, saying “we don’t accept that the murderers investigate themselves.” Meanwhile, they wanted the talks to be put off until mid-May so that student representatives not aligned with Ortega’s ruling party are involved.
Managua’s archbishop, Cardinal Leopoldo Brenes, has said he is ready to mediate any dialogue.
The country’s powerful private business lobby, which distanced itself from Ortega over the violence, has also signaled it is now ready to participate in the talks.
– Ortega’s grip shaken –
The protests that erupted on April 18 were the worst faced by Ortega in his last 11 years in power, badly shaking his tight grip on power over the country, one of the poorest in Latin America.
The spark was reforms to the deficit-stricken social security system, but the unrest quickly swelled on the back of widespread resentment of Ortega’s perceived authoritarianism.
The president, a former Sandinista rebel who has ruled Nicaragua for 22 of the past 39 years, made a series of concessions after sharp domestic and international criticism over the use of security forces to put down the protests, and curbs on independent media to report them.
The concessions included abandoning the social security reforms, freeing dozens of arrested protesters, lifting broadcast bans on private TV channels, and offering dialogue.
Many Nicaraguans, though — especially emboldened university students — want Ortega to step down.
A mass demonstration sponsored by the Catholic Church was to take place later Saturday in the Nicaraguan capital, with busloads of demonstrators being brought in from rural areas.