East Londonderry MP Gregory Campbell has said that dissident republicans have to end their terror campaign before dialogue can be considered.
Derry City of Culture boss Shona McCartney said her door was open to talk to those who had bombed her organisation's office on Wednesday.
But Mr Campbell said talks had to be "based on some sort of premise for a successful outcome".
No-one was injured in the bombing but several premises were badly damaged.
It was the second attack in a year on the office which is home to the team which is organising Derry's year as UK City of Culture in 2013.
On Thursday, about 250 people took part in a rally in the centre of the city to protest against the attack.
Church leaders, politicians, and representatives from the arts sector were among the crowd.
'Dedicated and determined'
DUP representative Mr Campbell said it did not really matter whether the vast majority of the community were opposed to the attacks because the people carrying them out were "dedicated and determined".
He called for a security response and for people in nationalist and republican areas to realise that they "hold the key" in bringing the perpetrators to justice.
He said virtually everyone was in favour of talks but not "an open-ended dialogue" that would take place while dissidents continued to target people.
"That may only encourage them. They may consider - well we have moved these people to talking to us while we are continuing our terror," Mr Campbell added.
"Yes, dialogue is good but it has to be on the basis that they stop the violence.
"People have been talking to them over the past two to three years and unfortunately it hasn't produced anything by way or results.
"They seem to be a hardened, fanatical group. We come back to this - when they are in prison, they cannot plant bombs."
The latest attack prompted a strong reaction, with Derry PSNI commander Stephen Martin describing those responsible as "crazy".
He added that it was only a matter of time before someone was killed in the city.
It is thought one of two dissident groups, the Real IRA or Óglaigh na hÉireann, were behind the bombing.