Turkey Prime Minister Tayyip Erdogan Umit Bektas/Reuters ANKARA(Reuters) - Turkish Prime Minister Tayyip Erdogan accused Israel on Saturday of having "surpassed Hitler in barbarism" through its attacks on Gaza, but warned Turks against taking out their anger on the country's Jewish community.

Erdogan continued to ratchet up his rhetoric against the Jewish State over its offensive, threatening to further harm to already badly frayed relations between the two countries, once regional allies.

Hours earlier Israel advised its citizens against traveling to Turkey, citing "the public mood" after attacks on Israeli diplomatic missions during protests in Istanbul and Ankara against the Gaza offensive on Friday.

Palestinian officials say more than 330 people have been killed by Israeli strikes launched in response to rockets fired into Israeli territory by militants loyal to the Islamist group Hamas.

"(Israelis) have no conscience, no honor, no pride. Those who condemn Hitler day and night have surpassed Hitler in barbarism," Erdogan told supporters at a political rally in the Black Sea city of Ordu.

He accused the United States of defending Israel's "disproportionate" tactics, and bemoaned the failure of the Muslim world to take a stronger stance.

But Erdogan did warn his supporters against taking their anger out on the country's Jewish population.

"I don't approve of any (bad) attitude towards our Jewish citizens in Turkey, despite all this. Why? They are the citizens of this country," he said. Around 17,000 Jews live in Turkey.

Protesters have taken to the streets of the NATO member's two biggest cities for the last two nights, and were due to return later on Saturday. Local media reported an explosion of pro-Hitler tweets and some liberal Turks reacted with outrage on Twitter when a pro-government newspaper printed a Hitler-themed crossword.

On Friday U.S. representative Eliot Engel urged Erdogan to act after the same newspaper published an open letter calling on Turkish Jews to apologize for civilian casualties in Gaza.

“The disgusting letter published by the Turkish newspaper Yeni Akit has no place in any society and only serves to put innocent lives in danger," Engel, the leading Democrat on the House Committee on Foreign Affairs, said in a statement.

Israel's Foreign Ministry said early on Saturday Israelis should "avoid non-essential visits" to Turkey or be especially vigilant and steer clear of anti-Israel demonstrations.

On Friday the ministry said it would pare back already an reduced staff at its embassy in Ankara and consulate in Istanbul. Erdogan is hoping to become Turkey's first directly elected president in polls due in August, and anti-Israeli sentiment flows strongly through the largely conservative Sunni Muslim voter base he will rely on to give him victory.

The two countries have seen their relations degrade sharply in recent years, reaching crisis point when Israeli commandos stormed the Turkish ship Mavi Marmara sailing as part of a flotilla challenging the Jewish state's naval blockade of Gaza. Ten people were killed.

Efforts to repair the damage had intensified in recent months after Israeli Prime Minister Benjamin Netanyahu apologized for the raid, but hopes of a rapprochement appear to be fading, after Erdogan said on Friday that relations between the two countries would not improve while he remained in post.

(Additional reporting by Ece Toksabay in Istanbul and Dan Williams in Jerusalem; Writing by Jonny Hogg; Editing by Andrew Heavens)