The Senate has ordered Immigration Minister Scott Morrison to tell Parliament about incidents involving asylum seekers at sea in a bid to end the government's information clampdown.

A motion moved by Greens senator Sarah Hanson-Young was passed with Labor support on Thursday morning, demanding that Mr Morrison table reports about on-water incidents within 24 hours.

The order follows Mr Morrison's refusal during question time on Wednesday to answer a question by Labor immigration spokesman Richard Marles about the reported arrival of asylum seekers in Darwin earlier in the week.