Israel has proposed paying compensation to relatives of Turks it killed during a raid on a Gaza-bound ship, in exchange for Ankara's help in indemnifying the Israeli navy against lawsuits, officials said today.

The offer, broached by envoys in Geneva over the weekend, included measures to improve relations between the countries, but appeared to have fallen short of Turkey's demand that Israel formally apologise for the deaths of the nine pro-Palestinian activists in May.

The Israeli prime minister, Binyamin Netanyahu, whose delegate to a UN investigation into the bloodshed attended the rapprochement talks, also faces opposition to such a deal from his hawkish foreign minister and government coalition partner, Avigdor Lieberman.

"We made a compensation offer, and asked the Turks to do what needs to be done to address our legal concerns. We also want to see them return their ambassador and allow us to appoint a new ambassador in Ankara," an Israeli official said. "For now, however, there are still big obstacles."

The draft offers Turkey $100,000 (£63,000) each to families of the men shot dead by Israeli marines during altercations aboard the converted cruise ship Mavi Marmara, and an Israeli expression of "regret" over the incident, Israeli diplomatic sources said.

Netanyahu's adviser Ron Dermer said today Israel and Turkey were discussing "the phrasing of a compromise that both sides can live with … [and] that will get our relations with Turkey back on track and remove the whole affair from the international agenda".

He told Israel Radio: "We must remember that there are those at the United Nations, there are forces which would like to see our personnel arrested. What is important to the prime minister is to protect the marines and commanders. We have said at every discussion, at every meeting, that the troops acted in self-defence – there's no question about it – and not out of malice."

Rattled over private war-crimes suits filed abroad against its military brass and politicians by pro-Palestinian groups, Israel has tried to stave off any similar Turkish actions in global forums by quickly setting up two internal investigations, the findings of which will become its submission to the UN inquest.

Turkey has dismissed the Israeli inquiries as insufficient.

The rapprochement talks followed the dispatch by the Turkish prime minister, Tayyip Erdogan, of planes to help Israel extinguish a forest fire last week. Netanyahu had pledged to "find ways to express our appreciation" to the Turks.

Erdogan, leader of the Islamist-rooted AK party – who is a frequent critic of Israel's Palestinian policies – signalled yesterday no flexibility in Turkey's terms. He even added an older demand that Gaza's Hamas-ruled borders be opened.

"If there are those who want to start a new period, I repeat: They must accept their guilt, apologise and pay compensation. I say too that the embargoes, which have been eased but not enough, should be lifted," he told AK legislators.

The Mavi Marmara led an aid-ferrying flotilla that tried to breach Israel's Gaza blockade, imposed with the declared aim of keeping arms from Islamist organisation Hamas. A worldwide outcry at the vessel's seizure prompted Israel to allow more goods to reach Gaza's 1.5 million Palestinians by land, but not by sea.

Among the most vocal champions of the blockade is Lieberman, who leads the far-right Yisrael Beiteinu party in alliance with Netanyahu's rightist Likud.

Political sources say Lieberman is often excluded from Israel's more sensitive diplomatic contacts.

Noting that several marines were injured in the Mavi Marmara raid, a Lieberman confidant said: "It's the Turks who should be paying us compensation, and not the other way around."

That foreshadowed a possible showdown in Netanyahu's cabinet should the proposed rapprochement deal be brought to it for approval.