ARLENE Foster has invited the mayor of San Francisco to learn about the IRA after the city honoured Martin McGuinness's "courageous service in the military".
The DUP leader said the posthumous honour for the former deputy first minister had caused a great deal of pain and offence.
Victims of IRA violence also criticised the award as "disgusting".
The certificate, which is the equivalent to the freedom of a city, also recognised the former Sinn Féin MP's role in the north's peace process.
An online petition demanding the city rescind the award had yesterday gained more than 1,500 signatures.
The award was approved by the Democratic mayor of San Francisco, London Breed.
It read: "Martin’s courageous service in the military and as a negotiator, helped cement and shape the Northern Ireland peace process and construct the Good Friday Agreement.
"His sacrifice and dedication to secure peace for his people is not only an inspiration to us all, but represents San Francisco values at their best. He leaves a legacy that embodies and celebrates the diverse history and strength of San Francisco and Ireland."
Mrs Foster has now written to Andrew Whittaker, the British Consul General in San Francisco.
"It is important the people of San Francisco know something of the reality of IRA terrorism and I have asked the consul general to pass on a letter to Mayor Breed which details some of the IRA’s activities and makes an offer for her to visit Northern Ireland and see how that terrorism still causes pain today," Mrs Foster said.
An event yesterday to mark European Day for Victims of Terrorism heard condemnation from victims.
David Kerrigan's sister Heather was a 20-year-old corporal in the UDR when she was killed in an IRA landmine blast just outside their home town of Castlederg, Co Tyrone in 1984.
Mr Kerrigan, who was on the same patrol and was badly injured in the attack, said: "Martin McGuinness wasn't in an army - he was a terrorist, he was the leader of the terrorists."
Mervyn Lewers, a retired policeman who lost both legs in an IRA under-car bombing, said he was "disgusted" by the award.
TUV leader Jim Allister, who hosted the event in the Senate Chamber, said: "We are here today to honour the victims of murder and of murderous attacks. We are not here to salute, to embrace the actions of victim makers, we are here to salute the memory of their many innocent victims."
Earlier, Mary Hamilton, an Ulster Unionist councillor who was injured in the Claudy bombing, and whose brother-in-law George Hamilton was shot and killed by the IRA in 1972, was also critical.
"I remember every day the Claudy bomb victims, blown to pieces at my feet, and my brother-in-law, shot in the back, and who left behind a four-year-old child and a wife and to think Martin McGuinness is being honoured," she told the BBC.
There was also condemnation from Ann Travers, whose sister Mary was shot dead in 1984 by the IRA, Margaret Veitch, whose parents were killed in the Enniskillen bombing in 1987, and Ann McCabe, whose Garda officer husband Jerry was shot dead by the IRA.