The two have met several times in the past, but it is thought the talks, which lasted 10 minutes, could lead to a landmark visit to the South.

The Monarch was at Queen's to celebrate the institution's centenary.

Historic

Afterwards, Mrs McAleese said an historic visit by the Queen to the Republic was significantly closer, but depended on the finalisation of devolution in Northern Ireland.

"I think the day is significantly closer," she said.

"We know that it is dependent on the completion of devolution, which hopefully will not be too far away. That means the return of policing and criminal justice responsibility to the Executive in Northern Ireland.

"When that is done, when devolution is completed, I think then anything is possible."

The meeting was the first the two heads of state have had in Northern Ireland.

"Both of us talked about how miraculous these times are in Northern Ireland," Mrs McAleese added.

Heaney

The Queen also talked with Nobel Laureate poet Seamus Heaney at the university as part of a celebration to mark the institution's 100th anniversary.

A centenary stone was unveiled by Her Highness and the Duke of Edinburgh in the Black and White Hall of the Lanyon Building.

It marks the granting of the Royal Charter to Queen's University in 1908.

The Centenary Stanza engraved on the stone was written and read at the ceremony by Seamus Heaney, a former student of the university and 1995 winner of the Nobel Prize for literature.

The visit came straight after a tour of the East Belfast Mission on the Newtownards Road in Belfast.

Hundreds of flag-waving supporters turned out at both events to cheer on the royal visitors.

Optimism

University vice chancellor, Prof Peter Gregson, said Queen's was "one of the best in the UK for knowledge transfer".

He added: "I have no doubt that the coming years will see a growth in the number of spin-out companies and high-quality jobs associated with them."

The event was the second centenary to have been marked by the Queen.

Last night, she attended a reception at Hillsborough Castle for the 100th anniversary of the birth of the Territorial Army.

Her Majesty was greeted by The Lady Carswell, The Lord-Lieutenant of the County Borough of Belfast.

On Thursday, the Queen will attend the Maundy Service in Armagh Cathedral.

Her Majesty was presented with a signed limited edition of The Blackbird's Nest, an anthology of Queen's poets, before meeting a number of students.

The Centenary Luncheon was attended by around 100 guests including the Former Archbishop of Armagh and Primate of All Ireland, Lord Robin Eames.

Archbishop emeritus of Armagh and primate emeritus of all Ireland, Cardinal Cahal Daly, was also there.

Following the lunch, Her Majesty met well-wishers in the cloister and was also presented with a posy by Rebecca Colquhoun, the chancellor's page.

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