He narrowly missed out on gold in the BC12/BC2 team event alongside David Smith, Josh Rowe and Claire Taggart, with the Great Britain team edged out on a tie-break by Japan in the final.
The match had finished 7-7, with a five on the fifth end for Japan turning the tie.
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The quartet had earlier won one and lost one of their pool games to qualify for the semi-finals where they beat Brazil 14-2 - the first time they had beaten the Paralympic hosts.
In the individual BC2 competition, Murray won his group to make it through to the knockout stages where he beat number two seed Robert Mezik of Slovakia 3-2 in the quarter-finals.
He was knocked out by Bernd Meints of the Netherlands in the last four, suffering a 5-2 defeat.
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He then faced GB team-mate Rowe in the bronze medal play-off and went on to claim a comfortable 7-1 success.
The Great Britain squad for the Rio Paralympics will be unveiled on July 15.