"We have no reason for friction with Turkey (but) an apology is not a compromise, it is a humiliation and it is an abandonment of [Israeli] soldiers. We regret the loss of life of people from any nation," Lieberman told the Knesset's Foreign Affairs and Defense Committee.
"There are things we can discuss and things we cannot. We cannot discuss things that will harm Israel. National honor has a real significance."
Nine pro-Palestinian activists were killed when Israeli commandos boarded the Turkish boat Mavi Marmara 13 months ago.
Vice Premier Moshe Yaalon is expected to meet with Turkish officials during his current visit to the United States and Prime Minister Binyamin Netanyahu sent Turkish Premier Recep Tayyip Erdogan a letter of congratulations on his re-election, Ynetnews reported.
Lieberman also threatened the Palestinian Authority with unspecified consequences for pushing for statehood at the United Nations.
"Unilateral steps will require unilateral responses," he was quoted as saying by The Jerusalem Post. He said the Foreign Ministry has "a variety of possible responses" ready.