Madrid moved second in the table behind Barca, albeit still six points back, with a derby defeat of their city rivals Atletico Madrid last weekend.
Barca's successive draws in the league have opened the door to Madrid, with Valverde's men having seemingly been on track to comfortably defend the title.
Captain Sergio Ramos said Madrid can catch Barca in the title race while goalkeeper Thibaut Courtois claimed teams will be "scared" of facing Santiago Solari's in-form side.
Valverde, however, noted Barca are still in a strong position to do the double again, having drawn at home to Madrid in the first leg of their Copa Clasico clash.
"Afraid of what? We compete against the same teams as ever for the league," Valverde told reporters on Friday.
"I always told news conferences I have a good relationship with the club so it came about naturally," he added. "The club made a proposal some time ago and I had some time to think about it and analyse our progress.
"We felt it seemed like a good time to make an announcement. We are all on the same wavelength at the club so it was an easy decision for me.
"Whenever you sign a contract with a player or manager you have the best intentions and high expectations but we all know football, it's determined very much by results.
"I assume that yes they trust in me to get those titles, but we know how capricious football can be. You don't always end up winning even if you think you deserve to."
Valverde, though, is fully aware his stabilised position at Camp Nou could come under threat at the end of the season if Barca
"If that happens then ask me again," he said. "But let's wait and see what happens first."