From BBC Alex Bogdanovic opens against Melzer on Friday, while Ross Hutchins and Jamie Murray have been named in the doubles.
"I'm confident I'll be able to handle the pressure," said Murray, 21.
Depending on the tie situation after Friday's singles, British captain John Lloyd could decide to pair Murray with his brother Jamie in Saturday's doubles.
Murray says he has suffered discomfort from a long-term knee problem because of the change of surface from hard to grass courts, but is prepared to play on all three days.
"I'll see how my body reacts to the first match but hopefully I should be OK (for the doubles)," he told BBC Radio 5 Live. ...... ................ Murray shrugged off the pressure, and hit back by citing Melzer's less than impressive Davis Cup win-loss record of 13-23.
Bogdanovic, Britain's number two, has never won a live Davis Cup rubber.
"This is my goal, to win a match in Davis Cup," said the 24-year-old, who lost 3-6 6-2 6-1 to Melzer in their only previous meeting - on grass in 2006.
"There's a lot of pressure on you. You're not playing for yourself, you're playing for your team and your country, and you want to do well. Every time you don't, you get down on yourself.
"It's going to be a difficult match for me but all I can do is try my best and see what happens."
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Friday 19 September 1100-1900, BBC Red Button and BBC Sport website 1100-1430, BBC TWO and BBC Sport website