Germany, Russia and Serbia have made solid starts in their quest to qualify for the revamped event's finals week in November.
Germany took a 2-0 lead over Hungary with ATP Finals winner Alexander Zverev, the only current top 10 player in action this weekend, beating Peter Nagy 6-2 6-2 after Philipp Kohlschreiber had given them the lead in Frankfurt.
World No.32 Kohlschreiber earlier rallied past Zsombor Piros 6-7(6) 7-5 6-4.
Dusan Lajovic and Filip Krajinovic put Serbia, who were missing Novak Djokovic, in complete control against Uzbekistan as they breezed past Sanjar Fayziev and Denis Istomin in straight sets.
Facing a Switzerland team without 20-time grand slam winner Roger Federer and Stan Wawrinka, a potent young Russian team surged to a 2-0 lead in Biel.
Daniil Medvedev fended off Henri Laaksonen 7-6(8) 6-7(6) 6-2 before fellow 22-year-old Karen Khachanov swatted aside Marc-Andrea Huesler 6-3 7-5.
Italy took a 2-0 lead against hosts India with Andreas Seppi and Matteo Berrettini scoring straight-sets victories against Ramkumar Ramanathan and Prajnesh Gunneswaran on grass.
Alexander Bublik and Mikhail Kukushkin helped Kazakhstan claim the first two points against Portugal.
World No.25 Denis Shapovalov gave Canada the perfect start against Slovakia on clay, defeating Filip Horansky 6-4 7-5.
However, the hosts hit back through Martin Klizan, who outmuscled Felix Auger-Aliassime 7-5 6-3 to level the tie.
China and Japan were also locked 1-1. China went ahead after Li Zhe beat Yoshihito Nishioka 6-3 6-2 win but Japan hit back through Taro Daniel, who beat Zhang Ze 7-6(3) 6-4.
The teams will play a doubles rubber plus two reverse singles rubbers on Saturday.
Brazil are all square with Belgium in their tie as are the Czech Republic and the Netherlands in Ostrava.
Dutchman Robin Haase levelled things up with a 6-2, 6-4 win over Lukas Rosol after Jiri Vesely had claimed the lead with a 5-7 6-4 6-4 success in his opening match with Tallon Griekspoor.
Winners of the 12 qualifying matches will join last year's semi-finalists - Croatia, France, Spain and the United States - as well as wildcard entrants Britain and Argentina in the finals.
