Mr Brown's future is the subject of several Downing Street petitions
Downing Street has responded to a petition signed by more than 72,000 people calling on Gordon Brown to quit, saying he is "determined" to go on.
A two-line response on the Number 10 website said the prime minister was "completely focused" on fixing the economy and improving public services.
It added that he would work for "a stronger, fairer, better Britain".
Another petition, which closes next May and calls on the PM "not" to go, has attracted 67 signatures so far.
The online demand for Mr Brown to stand down was tabled by Kalvis Jansons and had attracted 72,232 signatures by the time it closed on 22 October.
It read simply: "We the undersigned petition the prime minister to resign."
Mr Brown's office responded with the words: "The prime minister is completely focused on restoring the economy, getting people back to work and improving standards in public services.
"As the prime minister has consistently said, he is determined to build a stronger, fairer, better Britain for all."
Online Downing Street "e-petitions" began in 2006.
There are currently several posted on the subject of Mr Brown's future and those of some of his cabinet colleagues.