The Red Star One, its chartered vessel, has been waiting offshore from the besieged western city since Saturday. Two severely wounded people are reported to have died in hospital during that time while awaiting evacuation, the agency said.
Misrata port is a lifeline for the besieged city and has been under heavy bombardment by Muammar Gaddafi's forces. NATO minesweepers searched the approaches of the harbor on Monday for a drifting mine, blocking aid supplies.
"We are appealing to NATO and Libyan authorities to allow the ship to dock so we can evacuate these people who are around the port," IOM spokesman Jumbe Omari Jumbe told a news briefing.
Jumbe later told Reuters: "We will hang on there as long as it takes, until we get word from NATO that we can go in."
The Albanian-registered ship is carrying 180 tonnes of food, water and nappies for the western city's besieged population.
At least 23 journalists have requested evacuation as well as some 36 wounded people in Misrata, where intensive care units have run out of beds and supplies, according to the Geneva-based agency.
"Every second now counts. We need to get this boat into Misrata port today (Tuesday) because lives have been lost already while the boat has been forced to wait offshore," Mohammed Abdiker, IOM's director of emergencies and operations, said in a statement.
More than 1,000 migrants from countries including Niger, Ghana, Chad, Nigeria, Sudan, Mali, Egypt and Bangladesh are waiting at the port to be rescued, according to the IOM. They include some 71 women and children.
The agency has also heard about some 109 Filipinos seeking rescue from Misrata, including women and children, but had not been able to establish contact with them.
The IOM has already evacuated more than 5,500 people from Misrata. This is its sixth rescue mission there.
In all, around 12,000 people have been evacuated from Misrata by a dozen aid ships which delivered more than 3,000 tonnes of relief supplies, U.N. spokeswoman Elisabeth Byrs said.