Wales Women led twice but eventually had to settle for a draw in the first of two friendly matches in Slovakia.
Captain Jess Fishlock put Wales ahead after six minutes when she took a pass from Sarah Wiltshire to shoot home, but a defensive mix-up allowed Slovakia to score through Veronika Rybarova.
Helen Ward gave Wales the lead for the second time but Veronika Klechova struck back to rescue a draw.
The two sides meet again at the Senec Technical Training Centre on Wednesday.
Wales Women: Rhian Nokes (Cardiff City Ladies), Lauren Hancock (Cardiff City FC), Carys Hawkins (Sunnana SK), Lauren Price (Cardiff City FC), Kylie Davies (Chelsea), Angharad James (Bristol Academy), Sophie Ingle (Chelsea), Jessica Fishlock (Seattle Reign, capt), Helen Ward (Chelsea), Sarah Wiltshire (Watford), Natasha Harding (Bristol Academy). Substitutes: Alice Evans (Cardiff City Ladies FC), Sophie Cole (Cardiff City Ladies FC), Lauren Townsend (Cardiff City Ladies FC), Georgia Evans (Bristol Academy), Michelle Green (Cardiff City Ladies FC), Samantha Quayle (Bristol Academy), Hannah Keryakoplis (Liverpool), Catherine Walsh (Cardiff City FC), Emily Brown (Cardiff Met Ladies).