"We always thought of AAP as competition and we were expecting it to get double digit seats but this is surprising," BJP state president Vijay Goel told the media.
"We have done all the hard work in Delhi in the last 15 years but now AAP is reaping the benefits," he added.
Goel said he was confident the Bharatiya Janata Party would take power in Delhi.
"We will get at least 38 (out of 70) seats in Delhi and will form the government."
Election officials said the BJP was leading in 33 constituencies and the AAP in 26, relegating the Congress to a poor third at seven seats.
Four seats could go to independents and smaller groups.