Correspondents say his comments are intended as a message to ease anti-American resentment in strategically important Pakistan.
On Thursday Mr Kerry agreed to resume high-level talks over security issues.
The talks were stalled after 24 Pakistani soldiers were killed by the US on the Afghan border in 2011.
‘Sovereignty violation’
CIA drone strikes have killed up to 3,460 people in Pakistan since 2004.
Most strikes take place in the troubled border region of North Waziristan, which is regarded as an al-Qaeda and Taliban stronghold.
Prime Minister Nawaz Sharif, who won elections in May, met Mr Kerry on Thursday.
Mr Sharif has consistently demanded an end to such attacks, saying they violate Pakistan’s sovereignty.
His foreign affairs adviser, Sartaj Aziz, told reporters the US should stop the strikes “not just curtail them”.
Correspondents say the issue is complicated by the fact that some Pakistani officials have been accused of criticising the use of drones in public while co-operating with them in private.
‘Constructive and positive’
“I think the programme will end as we have eliminated most of the threat and continue to eliminate it,” Mr Kerry said in a television interview.
“The president has a very real timeline and we hope it’s going to be very, very soon,” he said when asked whether the US had a schedule for ending the strikes.
Analysts say his comments went further than those of President Barack Obama, who said in a 23 May speech that drone strikes would decrease in “the Afghan war theatre” as US troops withdraw by the end of 2014.
The number of strikes has fallen significantly over the past 30 months – totalling 17 so far this year compared to 48 in all of 2012 and 73 in 2011, according to estimates compiled by the New America Foundation.
Speaking after meeting Mr Sharif on Thursday, Mr Kerry said their talks were “constructive” and “positive”.
“We are here to speak honestly with each other, openly about any gaps that may exist that we want to try to bridge,” Mr Kerry said. “Our people deserve that we talk directly.”