The DUP has attacked Sinn Fein for meeting militant Palestinian group Hamas in an attempt to "wrongly glorify their own past".
In a departure from recent attempts to show a greater show of Executive unity, the DUP warned that Sinn Fein had regularly tried to use the international stage to justify its past violence.
Diane Dodds MEP also said the example of Northern Ireland showed terrorism could not win.
But Sinn Fein insisted its support of the right of the Palestinian people to self-determination would not waver.
Republican contacts with groups in the Middle East stretch back decades, with the party's MEP Martina Anderson also due to visit the central West Bank city of Ramallah later this week.
In 2005, Sinn Fein leader Gerry Adams met members of Hamas - the largest militant group in the region - in the Palestinian parliament and laid a wreath at the tomb of the former president Yasser Arafat.
The latest delegation to Istanbul at the weekend was headed by Sinn Fein's national chairperson Declan Kearney who met one of the main Hamas leaders, Musa Abu Marzouk, among others.
Mrs Dodds said: "These developments will not come as a shock to many. Sinn Fein have regularly sought to use the international stage to wrongly glorify their own past.
"The reality is that those they met in Istanbul have as their number one goal the destruction of the State of Israel. As recently as three weeks ago, Hamas are reported to have welcomed an attack on three Israeli soldiers at a checkpoint in Ramallah.
"Ironically this is the same place Martina Anderson intends to visit later this week, although if past experiences are anything to go by her entry may not be guaranteed.
"The Northern Ireland example highlights that terrorism does not win. Progress can only be truly achieved when all sides commit to exclusively peaceful and democratic means."
Ulster Unionist MLA Doug Beattie said, however, it was up to Sinn Fein to decide whether to meet Hamas or not.
"What I would say to Sinn Fein is 'if you think you have influence with Hamas, use that to persuade them to stop firing rockets into Israel'."
The Upper Bann MLA, a former soldier in the Royal Irish Regiment, added: "The bottom line is that they should be persuading Hamas to give up violence and to get around a table with Israel and negotiate.
"That is what the region wants. It is in the interests of the whole world, and it is exactly what Sinn Fein did themselves."
South Antrim MLA Mr Kearney said Sinn Fein outlined its experience of the Irish peace process to senior Hamas representatives and gave an analysis of the political situation in Ireland.
"We shared our view that Palestinian national, political and civic unity should be central to future political progress and that inclusive negotiations are essential to securing a peaceful, democratic, political agreement."