Clark said on Monday that she was encouraged by the words of regret from Israel's president but that New Zealand still wanted a formal apology.
Relations between the two nations have been frosty since two suspected Israeli agents were convicted and imprisoned in New Zealand for trying to fraudulently obtain a passport in 2004.
Wellington has demanded a public explanation and apology for what Clark described as "utterly unacceptable" behaviour by the two, Uriel Zoshe Kelman and Eli Cara.
They were deported last year after serving half of their six-month prison sentences. Police are still searching for several other people they believe were involved.
Clark has slapped diplomatic sanctions on Israel, including delaying approval of the appointment of a new Israeli ambassador.
She also postponed Foreign Ministry consultations and declined to issue an invitation for Israel's President Moshe Katsav to visit New Zealand.
New Zealand had slapped
diplomatic sanctions on Israel
Katsav said on Australian television that he regretted the deterioration of his country's relationship with New Zealand.
"I am very sorry about the last development in our relations with New Zealand." Katsav said on Channel Nine Television's Sunday programme.
"For us New Zealand is a good friend of Israel and I really regret what happened.
"But again, I really hope that this problem is closed and I want really to close this chapter in our relation with New Zealand. I can express my [sorrow] and my regret," he said.
Clark told TV One's Breakfast programme Katsav's comment that Israel wants to put the affair behind it means "I think we will make good progress in the negotiations".
But she said the comments were not seen by New Zealand as a substitute for the apology being negotiated with Israel.
"Obviously, the president's comments are encouraging and we are looking to progress the matter at a diplomatic level," Clark said.