UEFA President Michel Platini, a well-known opponent of using technology to help determine if a goal has been scored, also reiterated his opposition on Saturday following a UEFA executive committee meeting in Ukraine's capital.
The International Football Association Board (IFAB), comprising the four British associations and four members from FIFA, is expected to sanction the use of technology when it meets in Zurich on July 5.
UEFA have been experimenting with a five-man refereeing team, including two assistants who stand behind the goal, and UEFA want IFAB to endorse their system at the same time as delaying any decision on technology.
"We have evaluated 1,000 matches at the highest level and Pierlugi Collina, [UEFA's refereeing officer] showed us all the situations and benefits following three years of tests," said Infantino.
"The executive committee of UEFA unanimously agreed to issue a statement for full support for this system and to request to IFAB and FIFA to allow the five referees to officiate in the future.
"The results from these 1,000 matches were extremely positive and there was just one serious mistake. Unfortunately it happened during these Euros as we all know, but there was unanimous support.
"The executive committee is asking FIFA and IFAB to start an open debate about technology in football involving all stakeholders before any decision is taken in this area."
The one mistake came during Ukraine's match with England when a shot from Marco Devic appeared to be over the line before being hooked clear by England's John Terry.
Despite that, Platini said he remained opposed to using technology in the game.
"I am not just wholly against goal-line technology, I am against technology itself because then it is going to invade every area of football.
"The goal between England and Ukraine - it was a goal, OK? - and it's a mistake from the referee and he didn't see it. But there was an offside before then so if they have given offside we wouldn't have had the goal.
"So why don't we have technology for offside decisions as well. And what about Diego Maradona's "Hand of God" goal in 1986, why don't we have technology to see if Maradona handled it? Where does it stop? It won't stop. I am against technology itself."
The debate about goal-line technology has lasted for most of the last decade, but IFAB is expected to endorse two systems on Thursday - the Hawk-Eye and GoalRef systems - which have passed stringent tests to the satisfaction of the Board.
The Hawk-Eye system is a British one based on cameras while GoalRef - a Danish-German development - uses magnetic fields.
Each system is required to send an immediate message to a watch worn by the referee within one second of the ball crossing the line.
Any amendment to the law needs at least six of the eight members of IFAB to vote in favour which is widely expected to be the case in Zurich.
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