The Turkish Chief of Staff and the Foreign Ministry expressed their opposition to the request, while Hikmet Cetin, former NATO senior civilian representative in Afghanistan for nearly three years, indirectly supported it.
In an interview with Zaman daily, Cetin said restrictions regarding Turkish troops in Afghanistan should be reduced to a minimum.
However, he added no country would force Turkey to do so and Ankara would make its own decision.
"The Afghan mission is NATO's most significant operation. I repeated that restrictions were completely unnecessary even when I was representing NATO there," Cetin said.
Certain countries have self-imposed restrictions regarding the missions and region their troops will undertake and enter.
However, the United States, the Netherlands, Romania and Canada had imposed no such restrictions.
NATO suffered troop losses after it undertook the command of securing southern Afghanistan.
Because of this, contributing countries, including Turkey, were requested to send additional troops.
Cetin said: "Gen. Jones is right in demanding more troops. When I was in Afghanistan, I was saying that restrictions were unnecessary and strict policies were causing difficulties. Restrictions should be minimized."
Turkish Defense Ministry Rejects NATO's Request
The Turkish Defense Ministry released a written statement saying Turkish troops would not operate beyond Kabul and serve in different tasks other than their specified mission.
The statement said Turkish troops were currently operating in Kabul in NATO's International Security Assistance Force in accordance with NATO's operational plan and national restrictions specified by Turkey.