The move came a day after Turkish President Recep Tayyip Erdogan said his troops and the Syrian fighters they were backing could break into the Kurdish-controlled town "at any moment".
Turkish-backed Free Syrian Army fighters are seen as they advance in north of Afrin, Syria, March 8, 2018.
"We have besieged Afrin".
However, a spokesperson for the Kurdish People's Protection Units (YPG) troops, contradicted the claims.
On Saturday, the Britain-based Syrian Observatory for Human Rights monitoring group said the attacking forces "are now four kilometers (2.5 miles) away from the town of Afrin from the northeast, where there are intense clashes, air strikes, and artillery fire".
In his speech, Erdogan said the military operation would not end with the seizure of Afrin.
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"Today we are in Afrin and tomorrow we will be in Manbij".
On Jan. 20, Turkey launched Operation Olive Branch to clear YPG/PKK and Daesh terrorists from Afrin, northwestern Syria.
Turkey launched the assault into the enclave on January 20 to drive out Syrian Kurdish fighters that Ankara considers to be a security threat due to their links to outlawed rebels in Turkey. Where there are terrorists, we'll be there, he added.
The Turkish operation in Afrin will be completed by May, after which the military may look to move into Iraq, Turkish Foreign Minister Mevlut Cavusoglu announced yesterday, according to state news agency TRT World.
"We can start to hopefully work out some of the issues", the State Department Spokesperson said on Thursday, referring to the Turkey-U.S. tense relations of the past period.
Earlier this month, Erdogan accused US President Donald Trump and his predecessor Barack Obama of failing to tell the truth over US support for the YPG.