The decision to call off the tournaments at Indian Wells this week prompted confusion and frustration among some players.
Rafael Nadal was in California when it was announced the Indian Wells Masters and Indian Wells Open had been cancelled.
While the Indian Wells Open will not go ahead in March, the WTA chief would not discuss future events.
Amid concerns over the coronavirus, the Indian Wells Masters and Indian Wells Open have been called off.
There will be no 2020 Indian Wells title defence for Bianca Andreescu, who still has not recovered from her knee injury late last season.
Simona Halep and Angelique Kerber will miss the upcoming tournament through injury.
Petra Kvitova was unable to add a second Qatar Open trophy to the one she won in 2018 as Aryna Sabalenka emerged victorious in the final.
The Qatar Open final will pit the 2018 champion against a player making her maiden appearance at the tournament.
Sofia Kenin's poor results continued on Tuesday, but Ash Barty had few problems reaching the last 16 in Doha.
Elina Svitolina's start to 2020 has not gone to plan, a defeat to Amanda Anisimova the latest setback for the world number seven.