'DWTS' Gleb Savchenko Calls Ex's Claim Authorities Are Searching for Him a 'Total Lie'

Gleb Savchenko is firing back at his ex-wife's claim authorities are trying to track him down with their teenage daughter ... calling the allegation a "total lie" in a new court filing.

According to court docs obtained by TMZ, the "Dancing with the Stars" pro says Elena Samodanova knows where he lives and where their 15-year-old daughter, Olivia, is staying. He also says Elena and Olivia have spoken several times since Olivia decided she wants to remain in California with him.

Gleb specifically takes issue with Elena's previous claim that the Los Angeles County District Attorney's Office was "taking steps" to locate him and Olivia.

He says that characterization falsely makes it appear he's hiding with their daughter and avoiding authorities ... calling it "simply outrageous and a total lie."

Gleb says their daughter is nearly 16 and has chosen to limit contact with her mother. He claims Olivia changed her phone number herself and decided not to give Elena the new one.

As we reported, Elena says Olivia was supposed to return to Hong Kong July 9 but never came back. She says she can currently reach Olivia only through Instagram and does not know her current address.