She went on to ask them to help "in some small way by becoming a UKJF Member" at a cost of £50 a year.
The festival was due to take place at the north London theatre in November. Earlier this month the venue said it would not host six galas and 26 screenings because of the UKJFF's "inappropriate" ties to the Israeli embassy, and demanding that the UKJFF return £1,400 sponsorship it received from embassy in London. The festival refused.
But following interventions by Israeli ambassador Daniel Taub and Culture Secretary Sajid Javid, the theatre agreed to drop its opposition to the funding.
In a joint statement, the Tricycle and the festival said: "We hope to begin the process of rebuilding trust and confidence with a view to holding events in the future."
In her email, Ms Ironside said that the UKJFF would not return to the Tricycle until "our audience are ready", but said she hoped that the festival's long-term future lay there.
She wrote: "We truly believe that it is in the interests of all parties to be working with the Tricycle."
The festival will now be screened at more than 15 venues. New ones announced this week include the Curzon Mayfair, the London Jewish Cultural Centre in Golders Green, the Odeon in Muswell Hill, and the Everyman in Hampstead. Venues outside London will include Cineworld in Manchester, CCA in Glasgow, and MAZCC, Leeds.
National Theatre director Nicholas Hytner, who is Jewish, has stood by his defence of the Tricycle.
In a private email seen by the JC, he said: "The Tricycle's initial position did not amount, in my view, to anything like a boycott. I could not stand by and allow a theatre I respect to be misrepresented."
