The Chinese foreign ministry threatened retaliation after CGTN's licence to broadcast in the UK was suddenly removed by Ofcom on Thursday.
Students have been protesting the appointment of an Erdogan loyalist as the rector of Istanbul's prestigious Bogazici University, with some demonstrations resulting in clashes with security forces.
Official: Large car bomb kills 9 in Afghan capital
EU chief negotiator Michel Barnier announced the suspension on Twitter but said lower-ranking officials would continue discussions in the interim.
Only Peter Szijjarto tested positive and will be flown home alone. The rest of the Hungarian delegation will be flown back in a separate aircraft.
The peace talks could see the exit of American and NATO troops from Afghanistan after 19 years of conflict.
Tensions between the two powers flared for the first time in 45 years in June, culminating in a recent clash in which 20 Indian soldiers were killed.
Serbian President Aleksandar Vucic and Kosovo’s Prime Minister Avdullah Hoti both described the deal, a diplomatic boost for Donald Trump, as a "huge step forward".
As with the Hagia Sophia, the decision is seen as being geared to consolidate the conservative and religious support base of Erdogan's ruling party at a time when his popularity is under strain.
One F-15 fighter plane did briefly surveil the Iranian passenger jet from a safe distance but disengaged after it established it was a civilian aircraft, the US confirmed.