"Music is a wonderful language of tolerance and friendship, which brings people together," he writes.
"Your concert in Israel could have spread the message that solutions come from constructive engagement that leads to compromise and cooperation. Music should unite not divide and your performance in Israel could have contributed to the spirit of hope and peace in the Middle East.
"Boycott and hate on the other hand, represents hostility and intolerance and I was sorry to see that you have succumbed to the supporters of a small fanatic group of BDS (Boycott, Divest and Sanction) movement that denies the right of the State of Israel to exist and spreads hatred and animosity.
"I invite you to meet me in person to discuss Israel, its achievements and its role as the only democracy in the Middle East."
The Jewish Council of New Zealand earlier said that, in succumbing to pressure to call off the concert, Lorde had made a political statement.
Spokeswoman Juliet Moses said the singer would perform in Russia on her Melodrama tour and that despite that country's human rights abuses no one called on her to cancel that show.
"Likewise, she is not accused of complicity with Trump and his policies when she performs in the United States."
The Zionist Federation of New Zealand also said it was disappointed Lorde had caved into pressure from "those who wish to see the destruction of Israel".
"By singling out Israel amongst other nations whose human rights abuses make any that Israel supposedly commit seem a drop in the ocean, shows the double standards and discrimination towards the Jewish state of those in the BDS movement," the organisation said in a statement.
Variety reported Israeli culture minister Miri Regev wrote: "Lorde, I'm hoping you can be a 'pure heroine,' like the title of your first album, be a heroine of pure culture, free from any foreign - and ridiculous - political considerations."