"It's not possible for us to accept, to swallow the message John Bolton gave from Israel", he said.
Bolton said the U.S. would first seek assurances from Turkey that it would not harm the Kurds - for the first time adding a "condition" to the withdrawal.
President Erdogan publicly blasted Bolton in front of the parliament.
Speaking to reporters in Israel, Bolton indicated that USA forces would only be removed when Daesh militants are completely defeated, and when Turkey makes guarantees that it won't attack US-backed, Kurdish forces of the YPG.
Bolton and Pompeo have both insisted on protection for all of the SDF, whose estimated 60,000 fighters include Syrian Arabs as well as Kurds.
In Jerusalem on Monday, Bolton listed pre-withdrawal "objectives" - including the final defeat of Islamic State and protection of Kurdish allies - that went well beyond Trump's simple assertion that USA forces were heading home from Syria.
Bolton presented Turkish presidential spokesman Ibrahim Kalin with a document restating Trump's intention to withdraw USA forces but also insisting on protection for Kurdish fighters, said according to a person briefed by a senior administration official who attended the session, speaking on the condition of anonymity.
Initially, President Trump said he would pull 2,000 U.S. troops out of Syria within 30 days, but after strong objection from Middle East allies and others, he has backed down.
The piece set up a contentious day of diplomacy for Bolton and underscored the destabilizing impact of Trump's shoot-from-the-hip approach to foreign policy.
"The claims that Turkey targets Kurds in Syria are dishonorable, ugly, vulgar and defaming", Erdogan said. National Security Council spokesman said the two sides had a "productive discussion".
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Senior Kurdish official Badran Jia Kurd said the Kurds haven't heard directly from the U.S., only through the media. Erdogan said it's a lie that Turkey would target the Kurds in Syria but said preparations were almost complete for fighting what he called "Kurdish terror groups".
Kurdish officials have held conversations with Moscow and Syrian President Bashar Assad's government about protection, but Bolton called on them to "stand fast now".
The Trump administration encountered similar pushback elsewhere on Tuesday, as USA allies pressed their own priorities. America's Rachel Blevins has the details.
At the time, Trump had also said that Turkey would step up the fight against the remnants of the Islamic State in Syria, but Bolton said Sunday US troops will eliminate what remains of IS as another "condition" to northeastern Syria.
Bolton's delegation stressed that Washington was seeking a negotiated solution to Turkey's concerns and would cooperate with Ankara on deconflicting airspace over north-east Syria.
"We will be leaving at a proper pace while at the same time continuing to fight ISIS and doing all else that is prudent and necessary!" According to the Pentagon Monday, the coalition has signed off on a new conditions-based framework for the withdrawal that is now in effect.
In meetings with Turkish officials Tuesday, Bolton said he will seek "to find out what their objectives and capabilities are and that remains uncertain".
Bolton left the Turkish capital on Tuesday, leaving behind Chairman of the Joint Chiefs of Staff Gen. Joseph Dunford and Special Envoy for Syria James Jeffrey.
Bolton is visiting the region to assure allies that the United States is not abandoning them.