Barca's 3-1 success in Wednesday's King's Cup semi-final, first leg against Villarreal at the Nou Camp was their 10th consecutive victory in all competitions, their longest winning streak since the end of 2010.
As well as being on the verge of a place in May's Cup final, they are only a point behind leaders Real, who were thrashed 4-0 at champions Atletico Madrid last weekend, in La Liga ahead of Sunday's game at home to struggling Levante (1600 GMT).
"Yes, yes, without doubt the team can maintain this intensity until June," Luis Enrique told a news conference after goals from Lionel Messi, Andres Iniesta and Gerard Pique secured victory over Villarreal.
"I think it's feasible, that's why we rest players," added the former Barca and Spain midfielder, who left regulars Sergio Busquets and Xavi out of the side on Wednesday.
"We have been on good form throughout the season but perhaps now we are more refined. We can still improve in all areas."
Real coach Carlo Ancelotti, meanwhile, needs to work out why his players, who have a chance to bounce back in Saturday's match at home to promoted Deportivo La Coruna (1700), have lost their way since they set a Spanish record of 22 straight victories at the end of 2014.
Injuries have played a part, with centre backs Pepe and Sergio Ramos and midfielders Luka Modric, James Rodriguez and Sami Khedira all currently sidelined.
At the same time, top scorer Cristiano Ronaldo has gone off the boil and has only managed four goals since the turn of the year, a paltry return by his standards.
One Deportivo player who will not feature on Saturday is midfielder Jose Rodriguez as he is on loan with the Galician club from Real's B team and his contract prohibits him from playing.
"It makes me really annoyed," Rodriguez said in an interview with sports daily As published on Thursday.
"It's true that in general they (Real) have suffered a slump in 2015 but it's because they started very well and they can get back to the same level."
Atletico, three points behind Barca in third, play at Celta Vigo on Sunday.
(Editing by xxxxxxxxx)
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