In the rest of the UK, schedules are operating as normal.
Flights over Europe were banned last month because of fears of the effect of volcanic ash on plane engines.
The decision to lift the restrictions followed safety tests that showed the engines could cope in areas of low-density ash.
The fresh disruption on Tuesday came as European Union transport ministers met in Brussels to agree measures they say will help prevent further disruption to air travel as a result of volcanic ash.
The steps include speeding up current plans to integrate Europe's airspace, creating a "single European regulator for a single European sky".
The meeting follows criticism from the airline industry that governments took an over-cautious approach to the ash cloud crisis last month, grounding flights unnecessarily.
On Tuesday, the IAA (Irish Aviation Authority) said it had cleared Irish airports to open for full operations from 1300 BST and Dublin, Shannon, Cork, Knock, Donegal, Waterford and Kerry could resume normal operations.
Nats Director Ian Hall and latest footage of the volatile Icelandic volcano
Flights from the UK and continental Europe flying across the airspace have not been affected.
In the UK, the Civil Aviation Authority closed Northern Ireland airspace from 0700 BST until 1300 BST with Belfast International, Belfast City and City of Derry airports all affected.
The CAA said the affected Scottish airports were expected to re-open in the afternoon.
In a statement, the CAA warned that the situation remained "very dynamic".
It added: "Passengers expecting to travel from the impacted airports should contact their airlines to confirm their flight is operating."
The ban disrupted the plans of Conservative leader David Cameron, travelling for his first election campaign visit to Northern Ireland.
Liam Dutton of the BBC Weather Centre said the concentration of ash was expected to become thinner by the middle part of the day.
The Natural Environment Research Council was due to send a plane, which is used jointly with the Met Office, to look at the ash cloud from about 1100 BST. It is expected to be in the air for about four to five hours.
In a statement, the IAA said winds from the north could cause further problems later in the week.
"Our decision to close earlier today was based solely on the safety risks to crews and passengers as a result of the drift south of the volcanic ash cloud caused by the north-easterly winds," it added.
Irish Ferries said it had space on services between Ireland and the UK as well as Ireland and France.
Hundreds of flights have been affected:
flights to and from Dublin, Cork Shannon and Belfast airports to the UK and Europe scheduled before 1300 BST were cancelled.
flights into and out of Belfast, Derry City and the Republic of Ireland until 1400 BST were cancelled. As a result, the airline will put on extra flights later on Tuesday and Wednesday
services to and from Derry and Donegal airports were cancelled on Monday night
cancelled about 20 flights on services to and from Belfast City and Belfast International airports
which operates six UK airports including Heathrow, Stansted and Glasgow, advised passengers heading for Ireland to contact their airlines for advice
Edinburgh and Glasgow had a
departure and arrival service between each airport and Newark, New Jersey, cancelled
said its flights to and from Islay and Campbeltown were cancelled on Tuesday and services to Benbecula, Tiree and Stornoway were delayed until further notice
said it would be operating all its remaining flights on Tuesday as scheduled, following the lifting of the flight ban
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