The Group I match was paused in the 19th minute after a banner was unfurled by home fans in Bucharest which read: "Kosovo is Serbia."
Kosovo's declaration of independence from Serbia in 2008 is formally recognised by about 100 countries and the majority of European Union members though, but not Romania.
After discussions on pitch, French referee Willy Delajod then took the teams back to the dressing room, which led to a lengthy delay.
As the teams were leaving the pitch, Kosovo's Mergim Vojvoda appeared to make an 'eagle' gesture at the home fans with his hands.
Meanwhile, Romania's captain Nicolae Stanciu was seen trying to calm the home supporters.
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Chants of 'Serba, Serbia' were also reportedly heard, leading to conversations between team representatives.
After the removal of the banner, the match was allowed to restart at 0-0.
The two teams are currently competing for a place at next summer's tournament, with Romania behind group leaders Switzerland as things stand.
Kosovo have been playing friendly matches for the past 80 years, but only in the 2010s were they recognised by UEFA and FIFA.
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In 2016, Kosovo competed for their first World Cup, the Russia 2018 tournament, and have since attempted to qualify for Euro 2020 and the 2022 World Cup.