Turkish Foreign Minister Mevlut Cavusoglu's comments came a day after the U.S. and Turkey announced they agreed to form a joint operations center to set up the safe zone.
The announcement provided few details, but Turkish officials said the center would be set up in Turkey as soon as possible.
Syria's government, meanwhile, described the agreement as a serious escalation that violates its sovereignty. It said it was part of Turkey's "expansionist ambitions" in Syria, aided by Washington and its Syrian allies, the Kurdish-led forces.
The announcement of the new deal may have averted — for now — a Turkish incursion into that part of Syria.
Ankara seeks to push U.S.-allied Syrian Kurdish fighters out of the region as it considers them terrorists allied with a Kurdish insurgency inside Turkey.
The Syrian Kurdish fighters were the main fighting force on the ground against Islamic State militants in the area, and Washington has been hard pressed to protect its partners.
"We can define yesterday's agreement as a very good start," Cavusoglu told reporters.
But Cavusoglu added that his government will not let the implementation of this agreement stall like a previous deal with Washington reached last year.
"We won't allow this effort to turn into a new Manbij roadmap, to be a new delaying-tactic," he said. That deal had set a timetable for the Kurdish fighters' withdrawal from the town of Manbij, which lies on the western banks of the Euphrates River.
Turkey says the U.S. never kept to the promise regarding the fighters' withdrawal.
Turkey's Defense Ministry said the two sides had agreed that the safe zone would become a "corridor of peace" and that measures would be taken to ensure the return of refugees to Syria. It offered few other details.
Turkey has been pressing to control — in coordination with the U.S. — a 19-25 mile (30-40 kilometer) deep zone within Syria, east of the Euphrates River, and wants no Syrian Kurdish forces there.
In two previous military incursions, Turkey entered northwestern Syria, expelling Islamic State militants and Syrian Kurdish fighters from the area and setting up Turkish military posts there, with allied Syrian opposition fighters in control. Turkish troops also man observation points that ring the last opposition stronghold in the northwest — posts that are meant to uphold a now fraying cease-fire.
Meanwhile, Damascus said the Syrian Kurdish groups "bear historic responsibility" for the U.S-Turkey deal and urged them to drop "this aggressive U.S.-Turkish project" and align with the Syrian government instead.
Syria has had no presence along the Turkish border since 2012, when Syrian rebels and Syrian Kurdish groups took control of different parts of the region.
The deal to create a safe zone in the northeast comes as fighting in northwest Syria resumed after efforts to salvage a Russia- and Turkey-backed cease-fire crumbled.
Syrian government forces have maintained an intense air campaign that has enabled their troops to advance in recent days.
The Britain-based Syrian Observatory for Human Rights said at least 49 air raids were recorded by early afternoon Thursday in 10 locations, while more than 380 government mortar and artillery shells were fired.
The government-controlled Syrian Central Military Media said troops captured the village of Sakhr and a nearby hill a day after taking another village to the southeast. The government resumed its offensive Monday, accusing the insurgents of violating terms of a revived truce.
On Thursday, the U.N.'s special envoy to Syria said the collapse of the cessation of hostilities deal was "regrettable." Najat Rochdi said in a statement that many civilians who had returned home because of the lull are now "at great risk" because heavy attacks resumed.
The U.N. said more than 500 civilians have been killed since the escalation in fighting in late April. More than 440,000 were forced to flee their areas, becoming displaced in the already crowded area that is home to 3 million people.