London mayor Boris Johnson said he would provide half the money and wrote to transport secretary Geoff Hoon urging him to provide the remaining £15 million.
But the government said it has already given Transport for London (TfL) a "generous" funding package for the next ten years and it is for the mayor and TfL to decide on their priorities for transport investment in London.
The spokeswoman added that £45 million has already been provided towards the estimated £110 million total cost for the second phase of the extension.
The London Borough of Wandsworth joined the call for funding. In a letter to Hoon, leader Edward Lister said: "This is just about the best-value infrastructure project in the capital. The south London boroughs need this link to ease overcrowding on existing routes and cope with rising population."