The Libyan prime minister was attending the G8 summit at Lough Earne.
The Gaddafi regime supplied the Semtex explosive used in the IRA bomb that devastated the County Fermanagh town of Enniskillen. Eleven people were killed during the remembrance day service. A twelfth victim died after 13 years in a coma.
In his letter Gault wrote that he was disappointed that Zeidan would not be meeting victims' groups, on a visit that he described as a "momentous occasion in our country's history".
Libya supplied several tonnes of weapons to the Provisional IRA in the 1980s as "revenge" for Margaret Thatcher's support of the US bombing of Libya in 1986.
Libyan logistical support for the Provisionals included anti-aircraft guns, flame-throwers, rockets, Soviet-made grenades as well as enough rifles to arm at least two infantry battalions.
However, Gaddafi's supply of Semtex was his most significant "gift" to the Provisionals and the explosive was later used to set off many of the huge devices that devastated parts of London, such as Bishop's Gate and South Quay in Docklands.
Gaddafi's regime first started supplying the Provisionals with weapons in the early 1970s when the republicans' head of Sinn Fein finances was Joe Cahill.
But in the 1990s Gaddafi tried to reach out to the UK and rebuild relations. His government, via the UN, provided an entire inventory of everything the regime had given the IRA in the 1980s.
In his letter to Zeidan, Gault called on the premier to give his "immediate attention" to "legacy issues which, if unresolved, will mean that relationships … can never be as close as they have the potential to be".
His letter continued: "For our part, as families, we are keen to support the efforts of the new Libyan regime, and we rejoice that a warmonger and tyrant is no longer at the helm of your country and that a democratic process is on the cusp of being born."
A Downing Street spokeswoman would not confirm whether Zeidan and Robinson would discuss the issue of compensation at their meeting.
The spokeswoman said: "We are in touch with the Libyan regime about these legacy issues and these conversations happen at the highest level on both sides."
A number of victims of IRA violence during the Troubles have launched legal actions against the Libyan government for compensation, on grounds that the Semtex that was used in a number of high-profile bomb attacks had been supplied by the former Gaddafi regime.
The claimants include victims of the Harrods explosion, including a US citizen caught in the IRA bomb attack in Knightsbride, London, and other victims of other atrocities, both in England and Northern Ireland during the Troubles.
Sean Henry, manager of the Clinton Centre, a reconciliation initiative constructed on the site of the 1987 bombing next to Enniskillen's war memorial, also welcomed Zeidan's visit.
"Anything that sees people talking about a better future has to be positive. Talking is the only solution," he said.
He added that he would welcome an opportunity to strengthen links between Northern Ireland and Libya, as two countries emerging from violent histories.