Tebas said if everything continues to go according to plan in Spain, he expects the league to resume a month from now - depending on decisions by local authorities regarding the coronavirus pandemic.
"We would like to start on June 12, but it will depend on a lot of things," Tebas said in an interview late Sunday with league broadcaster Movistar.
"If we all continue to comply with the health safety measures, I don't think we will have any problems."
The league confirmed the positive tests on Sunday but said it was not going to alter the practice protocol that got underway last week. Players from most clubs began individual training sessions on Friday after nearly two months of confinement because of the pandemic.
The league said it will "continue to apply the back-to-training protocol" that was approved by government authorities to "guarantee the maximum safety of all players, coaches and club employees."
Tebas noted the "very low" number of positive cases and said it will be virtually impossible for contagion to happen during games because everyone involved will have been tested ahead of time.
"The matches are where there will be less risk," Tebas said.
The five players who tested positive will remain sidelined until they fully recover. They are all without symptoms and recovering from the disease, according to the league. They will be allowed to resume practicing after testing negative in two consecutive tests.
All other players tested negative, and the league said only three staff members of clubs tested positive after nearly 2,500 total tests were conducted.
"This is good news for the football industry and for Spanish society as well," Tebas said, adding the league had expected about 30 positive tests.
Players, coaches and club employees involved in the training sessions are being tested daily.
The league did not name the players who tested positive. It also didn't disclose their clubs, but Real Betis goalkeeper Joel Robles later confirmed he was among those with COVID-19. Spanish media said two other players were from first-division clubs, including Atlético Madrid defender Renan Lodi.
Atlético on Saturday posted a message on an official club social media channel with a picture of the Brazilian and the message: "Renan Lodi says hello from his home.
We will see you very soon on the field, Renan!" He did not practice as the rest of Atlético players resumed their activities on Saturday. None of the players who tested positive reportedly play for Barcelona or Real Madrid.
Barcelona was among the first teams to resume individual training on Friday. Real Madrid is expected to be back in action on Monday.
"Soccer is secondary right now," Madrid defender Sergio Ramos said.
"But it can serve as a distraction for the people who have been suffering." Tebas said he expects matches to be played every day after soccer resumes in Spain.
Barcelona captain Gerard Piqué said he hoped to have more time for players to prepare.
"A few more days of practice would be good for us, especially because of the risk of injuries," he said.
Spain this week started loosening some of the lockdown measures that had been in place since mid-March because of the pandemic, allowing soccer players to resume training individually at the teams' base camps.
The league sent clubs a detailed four-stage protocol for the return to practice. The individual training will be followed by smaller group sessions and then full squad sessions. (AP) APAAPA