MELBOURNE, Jan 17 (Reuters) - Alexander Zverev took time to warm up and had to dig deep against fellow German Daniel Altmaier in his first match of the Australian Open on Monday as the world number three kick-started his bid to add a maiden Grand Slam title to his Olympic gold. The 24-year-old Zverev defeated the 87th-ranked Altmaier 7-6(3) 6-1 7-6(1) under the lights at the Rod Laver Arena to set up a second round meeting against Australian John Millman. "Not much went to plan today to be honest except that I won," Zverev said in his on-court interview. "But that is how it is sometimes. It is the first round of a very long tournament and you are not always going to play your best tennis. "It was a good match for me to get into the tournament and hopefully the next round will be better." Zverev won the men"s singles gold in Tokyo in 2021 during a season which has by far been the best of his career. He also picked up five other titles during the year, including two Masters 1000 trophies and the season-ending ATP Finals. The 2020 U.S. Open finalist showed his frustration on occasions with double faults but was otherwise solid in his service games, facing only a single breakpoint in the entire match - which Altmaier converted to lead the third set briefly. Zverev, who hit 14 aces and committed six double faults, soon got the break back and then had four match points on his opponent"s serve at 6-5. Altmaier saved them all to force a tiebreaker but the tall German, whose best performance at Melbourne Park remains reaching the semi-finals in 2020, raised his level to get over the line and sealed the contest when his 23-year-old compatriot found the net with a return. "I played him a few times," Zverev said of Millman, who is ranked 89th. "I played him once at the French Open which was five-and-a-half hours, five sets, so ... yeah, he"s a very difficult player to beat "Hopefully it"ll be another fun one, and I"m looking forward to being back on court."