The Transport Secretary Chris Grayling said the strike was "futile", adding that he would have a "careful look" at how to deal with the situation when the dispute ends.
He told the BBC Radio 4 Today programme that he was not ruling any options in or out.
We are looking very carefully at how we take things forward. There are a lot of things to consider.
Mr Grayling said he was not happy with the performance of the railways in general but he could not deal with the problems until the Southern strikes ended.
He said he had asked Southern's owner, Govia Thameslink Railway, to attend fresh talks at the conciliation service Acas but Aslef had refused - a claim the union has denied.
REPORT: Southern trains ground to a halt for the third day this week as angry passengers staged a protest at Victoria station
Talks aimed at resolving the Southern Railway drivers' dispute are being held at the conciliation service Acas.
Frustrated passengers share their stories as the worst train strike for 20 years hits home.