Mr Cameron and Mr Kenny met in Downing Street in April David Cameron will hold talks with Irish Prime Minister Enda Kenny later in Dublin.
After the meeting, the PM will attend a state dinner with the Queen and Duke of Edinburgh, who are in the Republic of Ireland for a four-day visit.
Mr Kenny has told the Irish parliament he will speak to Mr Cameron about the release of government files on the 1974 Dublin and Monaghan bombings.
Victims’ relatives believe there was British state collusion in the attacks.
Mr Cameron met the Taoiseach in Downing Street in April, but this will be the pair’s first meeting on Irish soil since Mr Kenny came to office in March.
In London, the pair discussed the recent upsurge in dissident republican violence, but the Irish PM insisted the possibility of amending the terms of the UK’s financial bail-out for his country did not come up.
Following talks on Wednesday afternoon, Mr Cameron and Mr Kenny will attend an evening banquet at Dublin Castle hosted by Irish President Mary McAleese.
Both Mrs McAleese and the Queen are expected to make speeches.
No group claimed responsibility for the Dublin and Monaghan bombings in which 33 people died, but loyalist paramilitaries were blamed.
However, the Justice for the Forgotten campaign, which represents survivors, believes secret British files could reveal evidence that actions by security forces and police amounted to collusion.
The group wrote an open letter to the Queen, coinciding with her visit, in which it appealed through her to Mr Cameron, asking him to commit to “a genuinely significant gesture of reconciliation” by opening them up.
“Without this move, deeply troublesome questions remain unanswered,” the letter said.
The Queen’s visit is the first by a monarch to the Republic of Ireland since the country gained independence.
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