"What I need (to do) to recover is rest as my doctor has already told me but I'll try to leave that for later on," Del Potro said after practising with the team at Parque Roca, the venue for the tie.
"It's something beautiful to be able to play here in Argentina and I'm going to make the effort for the crowd and try to give my best," added the 2009 US Open champion, who had surgery on his right wrist in 2010.
Del Potro raised the alarm on Monday when he said his doctor had recommended a fortnight's rest after being troubled by his left wrist during the US Open last week.
The lanky 23-year-old is Argentina's number one singles player with Juan Monaco as number two. Carlos Berlocq and Eduardo Schwank make up their doubles pairing in the absence of the injured David Nalbandian.
Jaroslav Navratil's Czech team of US Open semi-finalist and world number six Tomas Berdych, Radek Stepanek, Lukas Rosol and Ivo Minar also trained at Parque Roca ahead of Thursday's draw.
The winning team will meet holders Spain or the United States in the final which Argentina will host if they go through.
Argentina, who have reached the final three times in the last six years but never won the trophy, and 2009 finalists Czech Republic have met twice before with one win each.